Heck, it's even shocking they do that, since the argument falls to "I am what I say I am", and anything else can be boiled down to that. No matter what proof you give otherwise, "I am what I say I am" trumps all of them. Just by them saying they are what they say they are, there's proof that's completely inarguable in their claim- you don't have telepathy, you can't conclusively say they're lying about saying they are this. And once they added "just saying it makes you one of us"- even if you DID have telepathy and can say "You're lying and I can prove you're lying about being in this group", it also comes to "but I say I am, so I am what I say I am", so the argument is lock-tight.