Has Carlssen explicitly said "This guy has cheated?"
He has only said "I cannot speak because I would be in such a big trouble that I am not willing to do so".
It is not so trivial as "prove it" when you only have a deep, serious, professional conviction.
How would you explain his reaction then?
He didn't explicitly said that, but he certainly implicitly said that, which is essentially the same in this situation.
Best thing would probably be some statistical analysis, and some likelihood of the moves made. And in the end, someone will probably conclude that there's a x% chance that cheating occurred.
With that said - at this level, I don't know how you differentiate true outlier moves, from the player just being incredibly apt at the game? I've heard that one way of identifying algorithmic / computer programs, is that the moves can extremely weird compared to what a human player would have done.