Chess.com doesn't ban people just because they play well against a much lower rated player. Their detection methods take that into account. They get banned because they're using outside assistance, like a chess engine. He can appeal and if he is in the 0.03% of people where there's been an actual mistake, Chess.com will restore his account, but you can tell from that percentage that Chess.com very rarely makes mistakes, and usually only when a person has to make a judgement call (which they work very hard to avoid).
My friend (2247) got banned after playing against me (665). I accidentally started rated match.
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I asked person to play chess with me recently. He didn't had the chess.com account so he made one, and played a few matches with randoms. His accuracy was high from the first match. Near 90. I observed his matches and while he was making best moves, but they seemed obvious. He did made some inaccuracies.
Yesterday I finally played with him, but accidentally started a rated match, and just after beating me he got banned. I'm wondering that he might have got banned for playing a rated match against me, given the huge elo rating gap we have.
I can't confirm for sure whether he was cheating or not but by the way he talks, it sure doesn't seem like he would be cheating. And also by observing his games I can't say for sure that he cheated, as I also can understand what he's going for by his moves.
Is there any way for me to know whether the ban was legit or was by a mistake because I started a rated match, and poor him got banned. Is it illegal to play rated match against your friends when your rating gap is huge? As I can understand, lower rated player will definitely lose, and higher rated player can increase their elo by doing this. If yes, then I don't think my friend deserves ban. I was the wrong person here for starting a rated match.