Well, I don't know where you trail ride, but if I don't have 100% control of my horse's shoulder or rib cage or hind end, we might go right over a bluff should something unexpected happen. If she spooks at a wild turkey or we flush out some pheasants, I'd like to know I can disengage her hind end before she decides to bolt or buck. So, yeah, I want to be able to control my horse's body parts. It is called preparation. Setting up for success. Whatever. I will spend as many countless hours as it takes to make sure my horse and I will be safe no matter where we ride. You say it like there is something wrong with that??
I didn't say you needed an arena. You can work with your horse anywhere it is feasibly possible. Even on the trail.
You can't have 100% control of your horse's body parts. You can, however, have training in place that will let you take over your horse's body parts (such as the case would be in the examples you gave ^^), but 100% control all the time just isn't possible. If it was, no one's horse would spook ever. Then we'd all complain about how dull our horses were!
ETA: OP, look up those Bombproof Your Horse books, they're really good. There's also some stuff from Clinton Anderson about problem solving on the trail.