I think natural horsemanship is the same ask, tell, demand that horses use in daily life. You don't really give the horse a choice in the matter, the same as a lead mare doesn't give a less dominant horse a choice in the matter. Watch a herd of horses as feeding time. If a less dominant horse challenges the lead horse for the food source, the lead horse will ask them to leave by pinning his/her ears and glaring at the other horse. If that doesn't work, he/she will tell him to leave by biting at the other horse. And if that doesn't work, he/she will demand that they leave by physically chasing the other horse off by what ever means necessary. We do the same thing, like with leading a horse. We ask them to move forward, if they don't move, we tell them to move forward, if that doesn't work we demand that they go forward. It's a conditioned response that with practice they eventually get to where when we ask they go forward. It's the same way horses teach each other what is acceptable in the herd. That's why there is always a dispute when you add a new horse to a herd, they have to figure out where this horse fits in the herd, your job is just to make sure that you are the dominant horse in the herd regardless of how many other horses are in the herd.
I guess in a way, it is a matter of choice for you and the horse. As in neither one of you have a choice in the matter of where you fit in the herd!