Well, that rings true to an extent for sure. The basic point being that competition introduces "real stress" (vs simple exhaustion). One of my favorite quotes (paraphrased) is from a motorcycle racer, talking about a persons attention capacity. Simply, that a person has "10 points" of capacity, and different activities, and events consume some number of points.
Consider a new rider trying to manage the combinations of the clutch, the gear shift, and throttle along with simple balance trying to get a bike moving. There's a lot going on, a lot of cognitive load. But, with practice, those actions become much more mechanical and automatic.
A person making a sudden stop on a bike, due to some emergent condition, a real beginner may simply slam on the brakes -- stopping the bike, but stalling the engine (since it's still in gear). With more experience, they'll know to at least bring the clutch in during the stop to avoid the stall, but end up stopped with the bike in high gear. Farther along, they find not only are they stopped, but the clutch it in, the engine is running, and they've shifted down to 1st gear, ready to move again. Even better, you may not have stopped at all but had the prescience and ability to avoid the event completely by maneuvering around it (which early on is not the intuitive reaction).
But you can see, when you're riding along and all of a sudden you have a eye expanding, aaooga horn blowing, "Tex Avery" style event, a lot of what you may have though was automatic may not be, especially if something goes wrong.
"A deer! Slam on the brakes!" but you hit the rear brake, not the front, now your back end is sliding around, which is unexpected, and your 10 point pool just got overflowed with 15 points.
When I see a racer, tucked in, knee down, in a 140MPH sweeping turn casually tearing off a face shield shade, you know that here's someone running along at 5 or 6 points of capacity... and how I'm not that guy! lol
These are the skills that get built up in competition. The repetitiveness of the stages building muscle memory and motor skills to the point that they can subconsciously "tap rack bang" during a failure. That the site picture naturally happens as soon as they raise the weapon, they not only focus quickly, but unfocus quickly, to help avoid tunnel vision etc. All of these things that can lower the "point cost" of fundamental skills and that can ideally be applied in a worst case scenario.
This is a lot different, I think, than just range time, since I think the clock and other pressures can add weight to the drills practiced. I have not done it enough on my own, and I'm not really fond of the idea of running clearance drills on my pistol while watching TV (though that's what some suggest, just to build muscle memory, build up hand strength, etc.) Just doesn't seem very fun!