How willing are we, normally, to lend credence to claims that have little to no corroboration? Do we approach similar claims differently based only on which ones we favor? We should be able to establish a pretty comprehensive sets of norms that most people can easily agree on.
Most people of faith have moved beyond what can be corroborated or not. Matters of faith have little to do with logic and appealing to the senses. Jesus himself said to Thomas, "because you see you now believe... blessed are those that believe without seeing".
Faith is tied to the heart and spirit, just as Jesus said. If one can believe that the heart and spirit exists (as opposed to nothing existing outside of hard solid tangible matter) then it's not a stretch to believe in the effect the gospels can have on that heart and spirit.