Bart D. Ehrman in Did Jesus Exist? (2012):

At the same time, the information is not particularly helpful in establishing that there really lived a man named Jesus. How would Tacitus know what he knew? It is pretty obvious that he had heard of Jesus, but he was writing some eighty0five years after Jesus would have died, and by that time Christians were certainly telling stories of Jesus (the Gospels had been written already, for example), whether the mythicists are wrong or right. It should be clear in any event that Tacitus is basing his comment about Jesus on hearsay rather than, say, detailed historical research. Had he done serious research, one might have expected him to say more, if even just a bit. But even more to the point, brief though his comment is, Tacitus is precisely wrong with one thing he says. He calls Pilate the "procurator" of Judea. We now know from the inscription discovered in 1961 at Caesarea that as governor, Pilate had the title and rank, not of procurator (one who dealt principally with revenue collection), but of prefect (one who also had military forces at his command). This much show that Tacitus did not look up any official record of what happened to Jesus, written at the time of his execution (if in fact such a record ever existed, which is highly doubtful). He therefore had heard the information. Whether he heard it from Christians or someone else is anyone's guess. (pp. 55–56)1