Theists: What makes your claims right and the claims of other theists wrong?

[Vicki Q]

But that's resolutely not what the disciples claimed happened.

Do you have any writings authored by any of the disciples so we may examine what they claimed?

There is evidence for a theory, which might or might not be true, that Peter was the primary source for Mark.

I'm not sure where you're headed with the question. Either there's a point I've missed completely, or you're unfamiliar with how secondary sources function within historical studies, in which case research would be both interesting and educational.