I've found that folks who make a big deal of the "tricks" like standing on the horse or sitting underneath them or laying them down and sitting astride them while they're down usually tend to skip over many of the basics. Their horse might lay down on command or stand still while you're standing on his back and swinging a tarp around but he won't stand tied, won't load in a trailer, won't stand for the farrier, and he bucks when you try to lope him.
There are many things with horses that do serve a practical purpose but, when they are used as "selling points", it usually means that the horse can't boast any real training.
For example, a horse that is comfortable with a person standing in the saddle. I've used my horse for a ladder on more than one occasion, but that's not something that I consider impressive. I'd much rather show off their spins or their cow-tracking ability.
I had to crawl underneath Taz when he was a yearling to remove the stitches from his hernia surgery. I had to get all the way underneath him because I couldn't see what I was doing from the side. That doesn't show any level of "training" or "bombproof" because he simply isn't. His training isn't perfect and he's certainly not even close to bombproof.
Just because I know I can do something doesn't mean it's good horsemanship to practice it frequently. Yep, I can walk under my horse but every time I do, it greatly increases the chances that something happens and I get hurt. The way I see it, going around the front or the back, I've got an exit route away from hooves. If I'm centered right between all 4 legs, then there is no safe egress if something happens.