The impulse can be seen in the modern apologetic as strongly as his predecessors from the very foundation of orthodoxy. The techniques are a mixture of special pleading, deliberate self ignorance, omission of inconvenient truths, use of long discredited arguments, and outright wishful thinking. There is an old saying about the most inquiring and intelligent believers that they "read themselves into heresy." But I have digressed too much already. It is better not to speculate how others think, and simply proceed with how I think and let things fall as they may. It's stupid to call your research complete and spend the rest of your life advocating, as most scholars do at some point or other. From that moment on it becomes a political game, the objective then seems to mirror to what Paul criticizes in Romans 3:19 ἵνα πᾶν στόμα φραγῇ.
But I am a from industry, not academia, and Demming's mantra rings true: you never stop tinkering, you improve, refine, and it something really doesn't work you redesign. For Bible research, its continuous testing and checking, in the spirit of John 8:32 καὶ γνώσεσθε τὴν ἀλήθειαν, καὶ ἡ ἀλήθεια ἐλευθερώσει ὑμᾶς. Enough of the pontificating, I just bored the heck out of myself.
Cornelius Tactitus Annals 15.44 has perhaps the most blatant of all insertions in the so called neutral independent witnesses. Below I give the text of the chapter (a few words adjusted to modern American English for clarity and accuracy. Everything from "But all human efforts" (Sed non ope humana) onward is suspect, and will be examined afterward.
44. Such indeed were the precautions of human wisdom. The next thing was to seek means of propitiating the gods, and recourse was had to the Sibylline books, by the direction of which prayers were offered to Vulcanus, Ceres, and Proserpina. Juno, too, was entreated by the matrons, first, in the Capitol, then on the nearest part of the coast, whence water was procured to sprinkle the temple and image of the goddess. And there were sacred banquets and nightly vigils celebrated by married women. But all human efforts, all the lavish gifts of the emperor, and the propitiation of the gods, did not banish the sinister belief that the conflagration was the result of an order. Consequently, to get rid of the report, Nero fastened the guilt and inflicted the most exquisite tortures on a class hated for their abominations, called Chrestians by the populace. Christ, from whom the name had its origin, suffered the extreme penalty during the reign of Tiberius at the hands of one of our procurators, Pontius Pilate, and a most destructive superstition, thus checked for the moment, again broke out not only in Judea, the first source of the evil, but even in the capital, where all things hideous and shameful from every part of the world find their center and become popular. Accordingly, an arrest was first made of all who pleaded guilty; then, upon their information, an immense multitude was convicted, not so much of the crime of setting fir to the city, as of hatred against mankind. Mockery of every sort was added to their deaths. Covered with the skins of beasts, they were torn by dogs and perished, or were nailed to crosses, or were doomed to the flames and burnt, to serve as a nightly illumination, when daylight had expired. Nero offered his gardens for the spectacle, and was exhibiting a show in the circus, while he mingled with the people in the dress of a charioteer or stood aloft on a car. Hence, even for criminals who deserved extreme and exemplary punishment, there arose a feeling of compassion; for it was not, as it seemed, for the public good, but to glut one man's cruelty, that they were being destroyed.
44. Et haec quidem humanis consiliis providebantur. mox petita [a] dis piacula aditique Sibyllae libri, ex quibus supplicatum Volcano et Cereri Proserpinaeque, ac propitiata Iuno per matronas, primum in Capitolio, deinde apud proximum mare, unde hausta aqua templum et simulacrum deae perspersum est; et sellisternia ac pervigilia celebravere feminae, quibus mariti erant. Sed non ope humana, non largitionibus principis aut deum placamentis decedebat infamia, quin iussum incendium crederetur. ergo abolendo rumori Nero subdidit reos et quaesitissimis poenis adfecit, quos per flagitia invisos vulgus Chrestianos appellabat. auctor nominis eius Christus Tibero imperitante per procuratorem Pontium Pilatum supplicio adfectus erat; repressaque in praesens exitiablilis superstitio rursum erumpebat, non modo per Iudaeam, originem eius mali, sed per urbem etiam, quo cuncta undique atrocia aut pudenda confluunt celebranturque. igitur primum correpti qui fatebantur, deinde indicio eorum multitudo ingens haud proinde in crimine incendii quam odio humani generis convicti sunt. et pereuntibus addita ludibria, ut ferarum tergis contecti laniatu canum interirent aut crucibus adfixi [aut flammandi atque], ubi defecisset dies, in usu[m] nocturni luminis urerentur. hortos suos ei spectaculo Nero obtulerat, et circense ludicrum edebat, habitu aurigae permixtus plebi vel curriculo insistens. unde quamquam adversus sontes et novissima exempla meritos miseratio oriebatur, tamquam non utilitate publica, sed in saevitiam unius absumerentur.
The context of this passage from Annals 15.38-45 concerns the great fire in Rome in 64 AD, and the subsequent reconstruction policies of Nero and their impact on the Rome, the surrounding Italian country and the reaction of the citizenry. Of note Tacitus gives considerable ink to the widespread notion that Nero himself was commonly suspected of starting or rather ordering the fire.
procuratorem Pontium Pilatum, which is the financial officer of a province, when in fact his position was that of "perfect" or military commander of the province (see Pilate Stone to left and note  below). It wasn't until Claudius that governors would be procurators as reported by Tacitus himself a few earlier (Annals 12.60). Its a subtle but strong argument (e.g., L.A. Yelnitsky) that suggests this is a later Christian interpolation, as it is hard to believe Tacitus would be so sloppy as to forget what he wrote a few books earlier about Claudius and procurators. So we have our first warning sign. It is also very out of place to bring up Tiberius who is nowhere in sight when speaking of Nero and his actions.
Josephus merely referred to Pilate as ἡγεμών or governor, which probably makes sense from a Jewish perspective. This general title was adopted by the writer of Marcion's Gospel and found it's way into Luke, and more tellingly as a pairing with Tiberius as τῆς ἡγεμονίας Τιβερίου Καίσαρος ἡγεμονεύοντος Ποντίου Πειλάτου τῆς Ἰουδαίας, but in the Latin Vulgate governor is translated procurator (!) imperii Tiberii Caesaris procurante Pontio Pilato Iudaeam, which is what we see in Tacitus essentially verbatim Tibero imperitante per procuratorem Pontium Pilatum ... Iudaeam! So what we see in fact is a Christian confession when combined with Christs passion eius Christus ... supplicio adfectus erat spliced into the same sentence. The only possible source is Christian literature, and only after translation from Greek to Latin.
Christianity is identified with a person named Christ and is called a destructive superstition exitiablilis superstitio which erupts again in Judea where it started per Iudaeam, originem eius mali. Superstition is equated in Tacitus with foreign religions, especially the Druids, but also with Egyptian and Jewish religions. There is often a description with the term of either the objectionable practice, such as the graphic description human sacrifice in Britain in Annals 14.30. Perhaps the closest similar description is in Annuls 2.85, where during the reign of Augustus where freed men of Egyptian and Jewish nationality are described as being infected with the worship of those lands superstitione infecta; but here the issue is not that of a religion proselytized to Rome, but rather that certain nationals kept the religion of their homeland, and would not renounce it now that they were free, and accept the cults accepted in Rome preferring their own. The passage in 15:44 however precisely concerns proselytizing, something without connection in Tacitus, but which is prevalent in Christians own self myth of their origins and growth, a concern that led to the writing of Acts of the Apostles and various others. The origin of this part of the passage is Christian as well.
|Sestertius, minted 64-66 A.D; Nero as Pontifex Maximus|
A Christian martyrdom theme permeates when Annuls reports "Mockery of every sort was added to their deaths" et pereuntibus addita ludibria. The language is derived from the Gospels account of the death of Christ, the mocking by the soldiers, as well as the inclusion of being crucified (crucibus adfixi) parallel all too closely to be coincidental (see Matthew 27:31, Luke 23:32ff, et al). The theme of martyrdom shows again in being covered in skins and torn by dogs, and must be from later Christian literature. Their selection as a sect was for their "hatred against humanity" odio humani generis convicti sunt, has the same phrase as Eutropius, Breviarium ab urbe condita 8.15, speaking on Commodus' death that he was as "as enemy of humanity" ut hostis humani generis. But the biggest problem has to do with being alighted (aut flammandi atque, ubi defecisset dies, in usum nocturni luminis urerentur). Such a horror as part of the "nightly vigils celebrated by married women" would constitute such an abomination that there is no way Tacitus or any Roman writer ever could restrain themselves from heaping derision at the pollution of such a sacred right by the Pontifex Maximus. This would have caused an immediate revolt. Contrast this absurd charge to what Suetonius wrote of the games which Nero hosted in De Vita Caesarum 6.12.1 "he killed no man, not even the guilty" (neminem occidit, ne noxiorum quidem). There is simply no way that such killing could have occurred and and escaped Seutonius' attention, and Tacitus would devoted two or three chapters covering such a disgrace and, rather than follow with a slightly glowing report of Nero's role.
Finally the very last sentence about Nero's cruelty, and about the compassion of the populace toward the criminals has to also be an interpolation. The focus of the chapter and the one which follows concerns the financial impact upon the Italian region for the reconstruction, nothing about any moral outrage.
So where did this passage come from? The answer can is seen dependence upon the the early 5th century work of Sulpicius Severus 2.29.1-3 concerning the fire in Rome 
Is the meantime, the number of the Christians being now very large, it happened that Rome was destroyed by fire, while Nero was stationed at Antium. But the opinion of all cast the odium of causing the fire upon the emperor, and he was believed in this way to have sought for the glory of building a new city. And in fact, Nero could not by any means he tried escape from the charge that the fire had been caused by his orders. He therefore turned the accusation against the Christians, and the most cruel tortures were accordingly inflicted upon the innocent. Nay, even new kinds of death were invented, so that, being covered in the skins of wild beasts, they perished by being devoured by dogs, while many were crucified or slain by fire, and not a few were set apart for this purpose, that, when the day came to a close, they should be consumed to serve for light during the night. In this way, cruelty tint began to be manifested against the Christians. Afterwards, too, their religion was prohibited by laws which were enacted; and by edicts openly set forth it was proclaimed unlawful to be a Christian.
Interea abundante iam Christianorum multitudine accidit ut Roma incendio conflagraret Nerone apud Antium constituto. sed opinio omnium invidiam incendii in principem retorquebat, credebaturque imperator gloriam innovandae urbis quaesisse. neque ulla re Nero efficiebat, quin ab eo iussum incendium putaretur. igitur vertit invidiam in Christianos, actaeque in innoxios crudelissimae quaestiones; quin et novae mortes excogitatae, ut ferarum tergis contecti laniatu canum interirent, multi crucibus affixi aut flamma usti, plerique in id reservati, ut cum defecisset dies, in usum nocturni luminis urerentur. hoc initio in Christianos saeviri coeptum. post etiam datis legibus religio vetabatur, palamque edictis propositis Christianum esse non licebat.This 5th century wording found its way into Tacitus, so complete that the ending passage about burning Christians as light fixtures is copied verbatim. We also in see in Sulpicius that same concern of Nero trying to shift blame for the fire. This blame is most likely posterior to Nero, and probably came about by way of typical Roman ironic political commentary about his ambitious rebuilding, and the resultant exorbitant cost of treasury (Annals 15.45) and need to plunder the surrounding countryside.
Unfortunately we are dealing with another Christian interpolation for everything above in blue. There is a strong 3rd century theme of Martyrdom, and strong association to the Gospel wordings, especially a Latin translation of Luke. While conservatively a date in the early 3rd century is possible, it is far more likely much later, as there is no Patristic reference in the first few centuries of such events, including Origen who compiled a listing of pagan mentions of Christians, knew Tacitus and yet didn't know of this passage. Not even Eusubius in the 4th century knows of it. I conclude that the most likely original reading excludes everything I colored blue. It is possible Nero probably did open his gardens to the married women's sacred vigils and the other ceremonies in an effort to counter rumors he had a hand in the fire, although it seems unlikely even that portion was original in Tacitus, since his estate was built on land claimed after the fire. But most certainly he never committed sacrilege on those women's ceremonial rites by burning humans on (Christian) crosses as the interpolation would have it believed. 
Postscript: Suetonius De Vita Caesarum 6.16.2
Just for completeness, the mention of Nero's new building codes for Rome (clearly after the fire) mentioned by Suetonius in 6.16.2, was obviously seen as the ideal spot to inject a vague anti-Christian "law" that just allows punishment, shown here:
Punishment was inflicted on the Christians, a class of men given to a new and mischievous superstition.What is of note are the words match almost verbatim with the interpolations Tacitus Annals 15:44: Suetonius afflicti suppliciis Christiani, Tacitus Christus ... upplicio adfectus erat; Suetonius Christiani, Tacitus Chrestianos; Suetonius genus hominum, Tacitus humani generis; Suetonius superstitionis novae ac maleficae, Tacitus exitiablilis superstitio. The dependence is obvious.
afflicti suppliciis Christiani, genus hominum superstitionis novae ac maleficae;
But there is another even more compelling reason to reject the phrase as an interpolation, as is stands isolated without context. There is nowhere in Suetonius in his want to gossip any further mention of Christians, even in respect to the fire, where he is want to quickly heap all manner of insults and accusations upon Nero, but no charge with respect to Christians. Moreover even within the laws reformed by Nero, there is no purpose served, no benefit, just a random listing, after a law to reduce excessive spending on public banquets, and before those against defrauding charioteers (cabbies of the day), ill behaving pantomimes (essentially street hustlers), forgers, illegitimate wills, limiting lawyer fees, finally cases connected with treasury be heard before a forum of arbiters. It's simply bizarre that there would be in this list of very sensible and popular reforms that vague punishments to some obscure religious sect would be of any interest to Suetonius or his readers. But it does make sense for the gossip minded Christian in later ages.
I conclude that Suetonius' report on legal reforms by Nero including vague punishments to Christians must be rejected as an interpolation on grounds of lack of context for their being reported, and also upon the literary dependence on the interpolations in Tacitus' Annals, which in turn is dependent upon Sulpicius Severus' work as well as the Lukan confession.
 The Pilate Stone from gives Pilate's title as perfectus which would be correct. However no artifact in the Judea from the first century is safe from pious fraud. This stone was reused as an amphitheater seat and so is the story for why it survived. While it's likely legitimate, I put no weight on it, but show it for the graphic.
 With Hochart, I see the dependence of Tacitus upon Sulpicius Severus (a work I only rcently became aware of) and not the other way around. It should be noted Tacitus Annals had only a single copy of survive in the 8th century, which all manuscripts we have are descendant. A single interpolation sometime between the 5th and 8th century could account for the passage. We should probably be grateful for the interpolation, as otherwise Annals might not have survived at all.
 P. Hochart in 1885 first suggested the passage was an interpolation. The grounds for an interpolation are laid out well in the alternative answer's fourteen points on this wiki answers page.