The proof was in the form of a world-record solve he did in competition, where he was at the end of a commutator with (I think) L D setup move, and he undid it as L' D', instead of D' L'. So then the corners were wrong when they were supposed to be solved. Instead of going on anyway - or fixing his mistake - he solved the corners using a 2x2 method, which would have totally messed up the edges. The point is that if he was not looking, and he realized he would have made the mistake, he would have fixed it with D L D' L'. That's the only way someone who was blindfolded could have fixed that error, if they noticed they had made the mistake. To have fixed it by basically starting over with the corners, doing things which would have messed up the edges (and, what, tracing half of the edges through the 2x2 algs he used?), there's no way he could not have been looking. You may have seen the quote "FRUR'U'F' is a Y-perm" - that's where it comes from, the competitor claiming that he knew it was a Y-perm, and so he could trace the edges through it. Of course that's ridiculous, that someone would make the solve so much harder for no reason, rather than just fixing the mistake with four moves.
Remember that this was before they used paper, so it was actually technically possible to look at the cube. After the cheating accusation, Ron tried to set up a meeting where they could at least prove (using the paper) that the competitor in question could do a fast BLD solve without looking, but the competitor *refused*.
And being 14 is not an excuse to be an arrogant thief... I was not like that when I was 14. People have brought things like that up before (someone even said that at that age he is too young to understand that cheating is wrong, which is 100% rubbish) and I don't agree at all.
watch out all Indian cubers!
so I need to switch soon. Which I will after my next exam!
