The same could be said for Arthur. Although proving he existed is never going to happen. A lovely myth probably based on a warlord and then, like Jesus, words were spoken, things were written and booom...the man, the myth. But, like Jesus, words were written quite a few years after the events. By word of mouth. A game of he said, she said.
Even in the middle ages only the clergy and top bananas could read, let along write. So history is kind of skewed. By the church/ winners. That kind of agenda is very hard to break into. A bit easier with Joan but there is still a hell of a lot of flim flam written and believed about her.
The Jesus thing blew up out of all proportion. Was there a Prophet? Sure. There were hundreds of them. Did he do miracles? No. But it's a very good narrative to fight the invaders. Based on someone? Definitely. Called Jesus? Not in any 'of the time' texts.