>if they have literal screenshots of the discussions between Niemann and chess.com admitting to cheating
Screenshots are easy enough to fake perfectly that if I didn't trust a party to give an honest summary of the discussion and (as in the current stake) thousands of dollars or more is at stake, then I wouldn't trust screenshots either.
Screenshots in this case are perfectly reliable. If they are literally faking screenshots of what Hans said, it'd be incredibly easy for him to prove it and sue them for the falsification.
Can you explain how Hans could prove that screenshots are fake? I suppose you mean Hans could subpoena records from his own ISP or Chess.com or Chess.com's ISP that reveal the content of Hans's communication; right?