I can sort of confirm that. I never learned all the formal theoretical standard chess strategies except for the basic ones. So when playing against really good players, way above my level, I could win sometimes (or allmost) simply by making unconventional (dumb by normal strategy) moves in the beginning - resulting in a non standard game where I could apply pressure in a way the opponent was not prepared for (also they underestimated me after the initial dumb moves). For me, the unconventional game was just like a standard game, I had not routine - but for the experienced one, it was way more challenging. But then of course in the standard situations, to which allmost every chess game evolves to - they destroyed me, simply for experience and routine.
IIRC Magnus Carlsen is said to do something like this as well - he'll play opening lines that are known to be theoretically suboptimal to take his opponent out of prep, after which he can rely on his own prep/skills to give him better winning chances.
You can score points against e.g. national team members who've been 5-0'ing the rest of the pool by doing weird cheap tricks. You won't win though, because after one or two points they will adjust and then wreck you.
And on the flip side, if you're decently rated (B ~ A ish) and are used to just standard fencing, if you run into someone who's U ~ E and does something weird like literally not move their feet, it can take you a couple touches to readjust to someone who doesn't behave normally.
Unlike chess though, in fencing the unconventional stuff only works for a couple points. You can't stretch that into a victory, because after each point everything resets.
Maybe that's why pentathlon (single touch victory) fencing is so weird.
Another thing he noticed is that, when asked to set up a game they were shown earlier, the errors expert players made often were insignificant. For example, they would set up the pawn structure on the king side incorrectly if the game’s action was on the other side of the board, move a bishop by a square in such a way didn’t make a difference for the game, or even add an piece that wasn’t active on the board.
Beginners would make different errors, some of them hugely affecting the position on the board.
Good ones are never randomly generated, however. Also, the skill doesn't fully transfer in either direction between live play and solving chess problems. Definitely not reconstructing the prior state of the board, since there's nothing there to reconstruct.
So yes, everything Hikaru was saying there makes sense to me, but I don't think your last sentence follows from it. Good chess problems come from good chess problem authors (interestingly this included Vladimir Nabokov), they aren't random, but they rarely come from games, and tickle a different part of the brain from live play.
It is false that GMs would have any trouble determining legal moves in randomly generated positions. Indeed, even a 1200 level player on chess.com will find that pretty trivial.
It's absolutely amazing to see a super-GM (in that case it was Hikaru) see a position, and basically "play-by-play" it from the beginning, to show people how they got in that position. It wasn't his game btw. But later in that same video when asked he explained what I wrote in the first paragraph. It works with proper games, but it rarely works with weird random chess puzzles, as he put it. Or, in other words, chess puzzles that come from real games are much better than "randomly generated", and make more sense even to the best of humans.