…and you’ve learned one thing: that a lot of people are telling similar anecdotes. (‘Rigorously’ assembling unsubstantiated stories doesn’t make the stories themselves rigorous; are trying to be tricky?) Presuming that these remain as ‘mere’ anecdotes (ie: lacking verification as to their veracity) the only further conclusion that you may draw from this accumulation of anecdotes is that as the number of them increases, the chances of their not being a related cause for them goes down. You learn nothing at all about wether they’re not all colluding, or independenly lying for similar reasons, or mistaking something else for what they all think they’re talking about…
If you’re only collecting anecdotes that agree with you, of course, the problem is worse by tenfold. I bet I could easily get ten thousand highly plausible anecdotes of people who flipped a coin and it came up heads. From all those anecdotes, can I conclude that all flipped coins always come up heads? Or even that they usually do?
Then they’re right. Of course, unless you go dig up a little more evidence than the mere relation of the anecdote, you’re not going to know that, are you?
There is a difference between proving something beyond a reasonable doubt, and proving it beyond all doubt, as you noted. Something can be extremely plausible to a reasonable person, and entirely false. Absent a legal context, I’d expect that ‘proof’ means ‘proof beyond all doubt’. Of course, I’ve taken more classes in logic than law, too.
The purpose of my example was to demonstrate that wether it’s one person or ten thousand claiming they talk to God, it’s not convincing evidence by itself, and it’s certainly not proof. Anecdotes have only rhetorical value; even in quantity; they prove nothing. As the claim becomes less implausible, the rhetorical argument becomes more believable, but that’s because it has less opposition, not because it’s a compelling proof on its own.
I will concede that there are situations where rhetorical arguments are effective; cases where there isn’t proof to the contrary being the most obvious example. Still though, absent independent confirmation that at least some of the anecdotes are true, they are not proof in any real form.