I think the term 'Natural Horsemanship' is a complete crock. There is absolutely nothing 'natural' about anything we do with any horse.
The first 2 things we do is take away their 2 'hard wired' natural instincts -- their herd instinct and their flight instinct.
It is not natural to take them away from their herd -- this is their whole world and their safety;
It is not natural to put restraints (like a halter) on horses and stop their natural flight instinct;
It is not natural to feed them anything but grass;
It is not natural to give them 'meals' instead of letting them eat as they want 24/7;
It is not natural to stuff them into a box stall;
It is not natural to put a saddle on one and get on his back much less, train it to do completely un-natural things;
Finally and probably most importantly, we have taken away 'natural selection' so instead of strong and hardy survivors being the horses that have reproduced we have turned breeding up-side-down by breeding for certain characteristics and ignoring the soundness, health and the well-being of the species.
So, to begin with, the term 'Natural' is total and complete BS where people enter the picture!
I think 'new age Gurus' coined the name to bilk thousands of people out of millions of dollars making them think they can teach them (the multitudes) to get their spoiled or untrained horses to be their servants and slaves by calling them 'willing partners' and pulling the wool over their eyes as to how they are making them (the horses) like it. But -- it is still BS.
What I have always thought is that breeding for 'trainability', willing disposition and usefulness and using training methods that built on a carefully laid foundation and by adding one small new thing at a time that the horse is ready to learn, we can 'teach' them what we need them to know to be useful to us.
If we do it right, it involves no force or violence or pain. We just teach a horse that if it moves from (yields) from pressure, we will take the pressure off. When they do the wrong thing, they run into pressure -- not punishment -- but just pressure. They do the right thing, the pressure instantly is gone, so they do the same thing the next time they feel the same pressure. This method used with 100% consistency produces a horse that has total and complete respect for a handler or rider.
Our selective breeding has given us wonderful prospects that do not resent working for us. We have bred horses that are willing, sensitive and have more ability to do greater things than any horses available to us just a few generations ago. The price they have payed for this selective breeding is that they are not a healthy, sound or hardy, they colic and founder more easily and they carry genetic defects that rarely showed up in 'natural' horse populations just a few generations ago. To me, this is the biggest price that horses have paid as a species. We are responsible and it is certainly not 'natural'.
Back to 'natural training'. A good trainer that has a good understanding of horse behavior uses pressure and the release of pressure to 'teach' the horse to do what is wanted. This is as far as 'natural' goes. Herd instincts use a great deal more fear and pain than a good trainer has to. A horse that does not instantly yield to the lead horse's pressure usually gets its butt tore up, gets bitten, kicked (sometimes resulting in a broken leg or other life ending injuries) and chased away from the safely of the herd. They can get run through fences and over crippling obstacles.
The best comparison between 'natural horse training' in a herd and training by an effective and good trainer would be what is required to 're-train' spoiled horses. [I guess the horse that stupidly tries to take the lead horse's grain would be considered a 'spoiled horse' of horse herd world.] I have not found an effective way that does not involve pain and/or heavy duty intimidation to break a bad habit and then some still return when the opportunity presents itself. This is why it is so important to not 'screw up' training a horse. It is MUCH more difficult to straighten up messed up horses than to teach them right the first time. It is why so many amateur trained horses get so spoiled.
What the term 'Natural Horsemanship' has turned into for some misguided people is to mean that only positive reinforcement is used (whatever that is) and that your pet, talk and reward with treats until the horse WANTS to do what you want it to do. This misguided non-method has produced many of the worst spoiled horses I have had to try to retrain. It produces many of the vicious horse that attack and injure people. It completely ignores the necessity of respect.
Respect results in obedience and getting the right result.
It is the trainer's responsibility to only ask a horse to do what it is ready and able to do.
It is the trainer's responsibility to ask in a clear and concise way so the horse knows what it is being asked to do.
It is the trainer's responsibility to not settle for less than what was asked. This is possible if the horse was ready and able to do it.
I would prefer to call good training like this -- 'Common Sense Horsemanship and Training' because it makes sense to the horse -- not because it is natural. It and no other 'training' is natural.