For sure you are correct. Just when someone says "mental" game, i was automatically not talking about the 15 vs 6 handicapper. Better mechanics will get you w/e flight or to the gross bracket in the tourney. But once the field is set, and aside from having the "shanks" that day, mental game may play a substantive role.
For me and my golfing buddies, i can say that this is absolutely not true. We have at least three guys in our group whose win rates vary wildly and consistently in weekend games vs "big $$" games. One guy is the below-average golfer usually, but for $$$ he seems to never pick up a penalty or 3 putt and 80% of the time he "outperforms". The other two always perform horrifically on those big days. This is over hundreds and hundreds of regular rounds, and ~25 "big" games. There's one guy who I honestly think has never come out cash positive in any "big" game... ever. But his index is about the same as all of ours.
Except you need no composure to hit a golf ball.
When I play, except on weekends, I walk from the car to the tee and hit the ball. I'm not composed at all, barely taking a practice swing and hit the ball pretty well, has nothing to do with my mental state.
I can't buy this. The" strongest mental player in the world" wouldn't have arrived there if he didn't have a sound swing! This is a false premise.
And yes, we've all seen guys wilt under pressure, especially in the later rounds. So, which is it? Mental or physical failure? I'd suggest that failure in the early rounds of a big situation is nearly entirely mental. In the later rounds, it could be either one. Especially if a player has been in a number of tournaments in a row. Mental and physical fatigue can set in at the worst time.