I would say there is more than a cheating history and a single game that triggered Magnus. However, most of it has a possible explanation. Like, I would be very nervous if you put me in front of a camera at 19 years. Are these arguments together strong enough? Hard to judge.
Do you have a link to this? Proof that this player has cheated in the past would be the strongest evidence, I believe, he'd do so again.
Having cheated in prior history is not a question, but the extent and recency of the behavior is.
Disclaimer: don't know much about chess, let alone professional chess.
I admit that it is a trickly problem, and I agree that Carlsen's behavior here is not beyond reproach. Withdrawing from the tournament only after having lost a game makes the statement much less impactfull since one can not discount the possibility that he's just being a rather sore looser. I would personally have respected his decision much more if he had followed his impulse (again, referred to in his statement) to withdraw as soon as Niemann had been invited to the tournament in the first place.