Hmm, I don't think this is related but I've personally witnessed (and even recorded) other people making MY moves in chess.com games and also I've been served up a game in progress and I've been able to make moves when I shouldn't have been able to.

There are plenty of threads about this too if you Google it. No idea if chess.com have fixed this in the last few months, but they didn't want to listen when I tried to report it.

All these games were when I was not logged into the site. It's never happened to me whilst logged in, but I don't play chess that often as it's no good for my blood pressure!