The point here isn't that people are nasty and that we have to deal with them. That's life and we all know it. But the fact is that chess.com has, in my experience, a lot more nasty people then their competitors. By in large I think its because chess.com has no enforced policy against threats, bullying, etc. Other places do.
This is exactly it. Every site has nasty people. But if Site A has a lot more nasty people that Site B or Site C, why would I bother to become a paying member of Site A? If chess.com took a tougher stance against cheating and verbal abuse, it would reduce these problems and attract a larger community. So it's in the interests of both the site and the members.
It'd probably be enough evidence. Probabilistically, matching a computer engine's top choice for every move in a game is orders of magnitude less than 1%. That's easily beyond preponderance of the evidence (in a civil case) or beyond a reasonable doubt (in a criminal case). There may be a question of admissibility, but I assume that's not the point of your question.