There is no exception here. The experience is unverified, ergo, it is not submitable as evidence.
Which denies a person the right to believe in what he has experienced, unless he can verify that he experienced it. Sorry, but your materialism denies the evidence of the senses.
After that, people who hear the story have a responsibility to judge it, based on what they know about the teller -- his closeness to the person who originally experienced it, his reputation for truth, etc. It may not be proof, but it is evidence.
Wrong again. They have every right to believe whatever they want to believe. Just because somebody tells me they had a personal experience where they "saw" the "Great Sky Fairy" does not make it true, no matter how much they [want to] believe it. Sorry, but you have presented no evidence, only hyperbole.
After that, people who hear the story have a responsibility to judge it, based on what they know about the teller -- his closeness to the person who originally experienced it, his reputation for truth, etc. It may not be proof, but it is evidence.
Incredible claims require incredible evidence to back them up. I would not care who told me about "The Great Sky Fairy", I would need more than anybody's testimony, regardless of who that "anybody" is, to accept that claim.