I’ve seen a video of Magnus Carlsen playing on Lichess before. Does Irwin ever accidentally flag him or people like him? Do these sorts of folks have to be verified in some fashion?
Not lichess, but Alireza Firouzja (World Rank #3) was banned from chess.com when he was younger. It was some time ago so probably their cheat engine detection, and also lichess's should give less false positives.
This has turned into a bit of an urban legend. The automated system flagged him based on both his rapid rise in rating and reports from several verified titled players.
On inspection by a human, he was cleared.
Danny exaggerates when he tells the story cause it's a funny anecdote.
This was also a very old version of the anti-cheat like you mentioned. Personally, part of the reason I prefer chess.com is their much better cheat detection than Lichess.