This is an extreme strawman that ignores logic.
Yes, we know from things like Acts of Pilate that Christians weren't above forging evidence but unless it directly dealt with Christianity such works were small; perhaps a paragraph or two.
They would NOT forge a work that for 99.99% of its text does NOT talk about Jesus as a way to show evidence for Jesus. No, on a practical level it would far simpler (and saner) to insert a paragraph or even better change a handful of words.
Jay Raskin pointed out the passage as it stands has problems: "Tacitus would have had to explain more about the suppression of the new superstition if it died out in the 30’s and started again in Rome around in the 60’s. (The Fire was in 64)."
However Josephus tells us of Festus' encounter with some robbers and it has been suggested the passage originally looked like this before the Christians tinkered with it:
"Consequently, to get rid of the report, Nero fastened the guilt and inflicted the most exquisite punishments on a class hated for their disgraceful acts, called Chrestians by the populace.
Chrestus, from whom the name had its origin, suffered the extreme penalty (i.e., Crucifixion) during the reign of
Nero at the hands of one of our procurators, Porcius
Festus, and a most mischievous superstition, thus checked for the 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 center and become popular."
Change those three names and Pestro chango you have a testimony for Jesus
Robert Van Voorst in his
Jesus Outside the New Testament touched on the idea of some Chrestus running around and in what has to be a prime example of hypocrisy dismisses it with an Argument from Silence. The VERY argument HJ-er deride mythers for using against Jesus is perfectly good to use FOR Jesus...HOW THE (bleep) DOES THAT WORK?!?
More over we see evidence that Chrestus is also used as a TITLE as well as a name so even if "Chrestus" wasn't a common name among Jews there is nothing preventing a Jew form using it as a title.