For me the important word in natural horsemanship is Horsemanship. Good horsemanship has been around since horses were first ridden. Bad horsemanship has also been around just as long. Natural Horsemanship to me is using the least amount of effort, force, pressure, whatever word you like to get the most positive results out of your horse. To always be striving for almost unnoticible stimulus or cues to the horse to get a positive reaction.
I'm terrible at articulating this stuff on a computer screen. Not much better in real life. Sometimes my horses don't have a clue what I'm talkng about.