That docetism lost out isn't really the key point.
Consider the general case: there's some property P that is observable (for example, having a physical body). At time T, there's no agreement that I have P. At time T+ 200 years, there's agreement that I had P at T.
It seems to me that the lack of agreement about P at T is important evidence here, regardless of what agreement other people come to about P at (T+200).
The people arguing not-P are theological mystics, who have substantial reason to assert not-P despite any observation, That is, a substantial amount of the motivation for asserting not-P can be explained without reference to observation.
I'm on shakier ground on the specific contents of the theological position, but Wikipedia leaves the impression was that the dispute was not about what was observed, but what was actually there. It seems consistent with docetism that Pilate believed there was a seditious preacher named Jesus, who he ordered crucified. Docetism just says that the image Pilate saw was an illusion, not a man (or even matter).
To break up the awkward silence at the start of a recent Overcoming Bias meetup, I asked everyone present to tell their rationalist origin story - a key event or fact that played a role in their first beginning to aspire to rationality. This worked surprisingly well (and I would recommend it for future meetups).
I think I've already told enough of my own origin story on Overcoming Bias: how I was digging in my parents' yard as a kid and found a tarnished silver amulet inscribed with Bayes's Theorem, and how I wore it to bed that night and dreamed of a woman in white, holding an ancient leather-bound book called Judgment Under Uncertainty: Heuristics and Biases (eds. D. Kahneman, P. Slovic, and A. Tversky, 1982)... but there's no need to go into that again.
So, seriously... how did you originally go down that road?
Added: For some odd reason, many of the commenters here seem to have had a single experience in common - namely, at some point, encountering Overcoming Bias... But I'm especially interested in what it takes to get the transition started - crossing the first divide. This would be very valuable knowledge if it can be generalized. If that did happen at OB, please try to specify what was the crucial "Aha!" insight (down to the specific post if possible).