I hate the term "natural horsemanship" for the above reasons but until people come up with a better one to describe this particular ethos of training, I feel we are stuck with it. When I have to define it, I say that it is a system of training a horse which takes into account horse psychology and body language, attempts to emulate how they communicate with each other, and offers alternative methods to the "traditional" ones for forming a relationship with the horse.
I have seen horse "free-lunge" each other. If you turn a new horse into a field, or put a couple horses together who don't know each other, the alpha horse will drive the beta horse away until the beta horse submits. Also, in the situation where you introduce a new horse to a herd, frequently the alpha horse will keep the new fella away for a few days, or even weeks.