I have heard a concrete allegation that in the Capablanca Memorial 2022 tournament (which was over the board), Niemann has games where he plays normally up to a point in the midgame, then he plays the top line of a specific engine (Stockfish 11) for an implausible number of moves in sequence.

There are a lot of lower-quality accusations, but this is the interesting one IMO. It should be easy enough to independently check for someone who has a setup for that sort of thing.