I am a long time follower of "natural horsemanship" in reality that title is more than anything a marketing device. The idea is to communicate with your horse in a way that, as closely as humanly possible, is the same as horses communicate with each other. Which in all honesty is what all good trainers are trying to do, be understood by their horse, whether they call it natural or not.
Many people get the wrong idea that you never reprimand your horse in NH "or you'll ruin your relationship", in my experience if you do not exert dominance over your horse you can't get the bond of real trust and friendship everyone seems to be trying to sell. Sometime to exert that dominance you do need to apply physical correction(I don't mean beating them) in the same way a dominant horse will apply physical pressure to horse that is not complying with the herd.
As far as bits being abusive, I'm on the fence about that one. I watched a video that showed lab experiments of the amount of pressure exerted on different areas of the horse's head and mouth when and 8yo child was using the reins on a simulated horse. It wasn't pretty, and made me VERY conscious of how I use my reins. On the other hand, MOST of the NH trainers do not condemn bits, and use them when riding their own horses. When they promote the use of a rope hackamore it is to keep unskilled hands from ruining a horse's mouth. In essence they are trying to train the human, and keep them from ruining the horse in the learning process.
NH has been a lifesaver for me, I did not have good role models with horses when I got my first horse, so having a vast array of NH trainers putting out books and videos really helped me. Now, that I have seen some really talented "normal" trainers, there isn't as much difference between the two as I had originally thought. It all comes down to good horse sense.