You're using logic to counter belief. It's not going to work.
Also, Randi is not an impassive man of science and logic. He is trolling the believers, and trolling them hard. It is a thing of beauty, because people who tend toward logic will be on his side without even needing to see someone refuse. People who believe will get all frothy in the mouth and argue any shred of evidence that his methods are not "fair" or "real science".
When someone claims psychic powers, implicit in their claim is that they can do this only in their own way, and not by some artificial method corrupted by some contest and its rules. If I can give you a cold reading after sending people to mingle with you n the lobby and feeding me details, then that is what I claim. Only, since I have no reason to state what should be obvious (I repeated on stage exactly what you told someone in the lobby), I only claim the supernatural part, that I can cold read you.
Make no mistake, Randi is most definitely being a showman with this claim, and it *is* set up so that anyone who accepts the challenge will fail. Not because he sabotages their performance, but because he removes the air of mystery. Mistakes can't be glossed over, preparation work will be revealed, and all opportunities for trickery are eliminated.
Once you prove something, there is no room for belief. Make no mistake - even if someone were psychic to maybe 75% certainty on a coin toss (50% better than expected) they would not be rigorously tested. Because with belief, you can get that number up to "almost 100%" because people stop counting. With logic, the counting never stops. This is why I believe no one will ever claim his prize, *even if they are legit*.
Randi knows this, he is a zealot on the other side, and he is trolling hard.
Doesn't make him any less right, it just puts him clearly in the realm of logic, not belief.