I did not read it but I will if it has bearing on our debate. Pax you did not tell me whether you believe other chronicles from Tacitus have verasity or not.
Well; Tacitus treated of the history and politic of the Roman Empire, so, things that were more common knowledge.
Furtheremore, the period his work covered started in 14 AD and he actually had met many of the actors of the events in question, or was once or twice removed from them.
We also have many corroborative evidences for the events he describes, from the works of other contemporary historians, for example, such as Pliny, as well as archaelogical evidences such as coins, steles and such.
Tacitus also generally mentions his sources, other historians, or official documents.
Even then, when essentially considered quite reliable, historians have debated his accuracy over some points, the annals, in particular, seem to be considered the less reliable of his work.
It is never black and white, you see, even when historians consider a source generally reliable, they always approach it with a grain of salt, especially in the cases when corroborative testimonies are not available.
Finally, there are some arguments that the whole quote may actually have been a later addition by a Christian scribe, like the most famous one in Josephus almost certainly is.
It is a minority opinion though, most people considered that 'Chrestians' were indeed in Rome at the time and that Nero blamed them for the fire. Tacitus, knowing about the Christian beliefs in Jesus martyrdom, would have made a passing mention of it, but did not feel it worthy of further investigation, his purpose was Roman politic after all, not the Religious sects of the Middle-East, and the idea of a Jewish prophet being executed was not one to raise any suspicion; they literally were using them to ornate his roadways.