Actually it supports the fact that by the time of the great fire in Rome (64 CE), there were Christians in Rome who were generally despised and therefore good scapegoats for Nero who wanted somebody to blame the fire on. Tacitus wrote all this about half a century later (116 CE). The whole passage reads:

Consequently, to get rid of the report [that he had caused the fire to be set], Nero fastened the guilt and inflicted the most exquisite tortures on a class hated for their abominations, called Christians by the populace. Christus, 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 Pilatus, and a most michevious superstition, thus checked for a moment, again broke out not only in Judea, the first source of the evil, but even in Rome, where all things hideous and shameful from every part of the world find their centre 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 firing 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, thet they were being destroyed.

Tacitus, Annals, 15.43-45, New York: Modern Library, 1942:380-1.

It would appear from the whole that the rise of Christianity owes not a little to Nero, the emperor everyone loves to hate. Certainly Tacitus does not have much sympathy for these dregs of all things hideous that drift into Rome: had they been killed off more gently he would probably not have turned a hair and public sympathy not aroused on their behalf. Had Nero (and some other of the nuttier emperors) not been such a monster, Christianity could well have fizzled out by the third century or remained a lunatic fringe minority faith, of which the empire had scores.