In fact, one of Ehrman's academic specialties is disciplined analysis of oral histories. A compelling argument he makes for the historical existence of Jesus is that we can see the material that made it into the gospels is oral history that behaves like real oral history should behave. (Meaning in short that the gospels themselves reflect certain changes to their fact-based accounting based on their author's geographic location, ideology, time of writing, etc. In a manner that's completely consistent with oral history evolution but not consistent with intentional fiction, which is generally more internally cohesive than the gospels are.)

He argues further that examining extra-canonical contemporary sources strongly supports an ordinary evolution of oral history based on a set of things that actually happened. I'm talking about gospels that didn't make it into the canon, and also the writings of church fathers in the first three centuries of the church.

According to almost all historical-critical New Testament scholars, oral-history analysis represents extremely important extra-Biblical evidence that Jesus lived. They also claim that the evidence can give us pretty good ideas of what the historical Jesus was actually like, though that's a lot more contentious.

The oral-history argument is harder to explain to people, but in the end, it's a lot more powerful than Josephus, which is pretty hard to accept as genuine on the evidence we have.