No one is talking about the other Gospels. Only one: Mark, written 30 years after the events. Not long enough for 'myths' to creep in and there were still witnesses alive to correct any errors. After 2,000 years, there is no evidence that contradicts it. All evidence discovered only verifies the account. Biblical and non.
Nothing that comes after that era is reliable, so the real question is, what in 2,000 years have we discovered that is contemporary with or very soon after Jesus's time? And the answer is: very little. I don't think the question of contradictory evidence is as much a closed matter as you do, both because it's very difficult to find texts from that time, period, but also because Christianity won the day, making contradictory narratives even more difficult to find. We know that, for example, during the time of Muhammad, all manner of Jewish and Christian writers wrote large texts in opposition to him, but very, very few of them remain (and that's from a time when texts were much more easily preserved than they were during the time of Jesus.)
As for witnesses correcting errors, you're assuming that Mark was written in order to be a historically-accurate document, whereas we already know that this is not a safe assumption to make when it comes to the formation of a faith-based belief system. Many of the writings during Muhammad's time, for example, already attribute to him things that simply go against science and our modern understanding of the world, and are thus not obviously historically-accurate- the myths were already creeping in while he was still alive. I'm not willing to simply accept the assumption that Mark was meant to be accurate in a historical (rather than a faith-based) sense. One story simply isn't enough to say much either way.
Tacitus' account betrays his unfavorable view of Christians so there's no reason to believe he'd bother to listen to their side, read their Gospels or pay them any mind.
What other sources would he have had? Especially since he doesn't mention them, we can only assume he is either using documents or hearsay- which is what most ancient historians used, isn't it?