My experience with a Morgan trainer was absolutely horrifying, I hope Dan's was not. Nails under the shoes (to encourage them to pick up their feet smartly), ginger applied to the anus to hold their tails up, whips, riding with a section of garden hose instead of a crop for better response(because the horses had been beaten with one - they leave less bruising). Soring. Peppermints to hide the odor of drugs on their breath. The little kit of injectable drugs I would run across occasionally, the laughing reply of the need to pep up the old ones and calm down the young ones. I could go on.
To me, there's no need to have the "natural" in front of horsemanship. It's either horsemanship, or it isn't. A horseman looks to his/her horse's needs first, and goes about training (regardless of discipline) in a way that makes his requests clear to the horse as gently as possible and as firmly as necessary.
Modern BNT's preach this concept, and countless others around the planet and for centuries have practiced it. It isn't about the specific method, it's about truly understanding the horse inside and out, what makes him tick, why it's biomechanically better for him to move this way or that, and learning how to influence his thoughts and actions without causing him undue physical or mental/emotional stress.