The truth is Traditional and Natural horse training are both "pressure and release" training. It doesn't matter whether the horse respects or fears you. The horse does the behavior asked of them because if they don't something they don't want will happen.
You are SO, SO wrong. This statement tells me that you know absolutely nothing about 'real training'. A horse doing what a handler / rider wants out of fear is entirely different from a 'trained' horse that is doing what it is supposed to because it respects the handler and has been trained and 'conditioned' to do what the trainer wants it to do. Good training and teaching has absolutely nothing to do with fear. Retraining spoiled horses? Maybe a little fear in the beginning, but not for very long.
I would doubt that you have ever been around a 'good trainer' and I doubt that you have ever ridden or handled a really 'well-trained' horse. As long as you are asking nothing more out of a horse than one would ask out of any companion animal, one is not teaching much.
Horses doing anything out of fear is so completely different than one responding because it has been 'conditioned' and 'taught' to respond are as different as night and day. They are in no way even similar.
I would say horses are working out of fear if I had to pick one - not panic, but they are working under the constant threat that if they don't respond correctly they will be progressively be made less comfortable, have to work harder or be in pain.
This is simply NOT how horses think and respond. Horses live 'in the moment'. Just like they do not stand around and worry about dying from some obscure cause. They do not think, "Gee, if I do not do this, Bozo here is going to hit me or make me miserable".
Good training by good trainers is no different than your 'clicker training' in that it 'teaches a 'conditioned response'. When the conditioned response wanted is something very simple or a 'trick', I can see where a clicker can produce the wanted conditioned response.
When a trainer is training a horse to do complicated things under saddle, I cannot see how the desired conditioned response can be attained by establishing a target or using treats. In 55 years, I have never seen it done with horses.
Other animal species have a lot more reasoning intelligence than horses do. Even donkeys do much more reasoning. Dogs and pigs do much more reasoning. The more reasoning intelligence an animal has, the more they can plan and project future consequences. Horse are in the here and now. Horses are 'creature of habit' much more than creatures of 'great intellect and reasoning'.
Can they be fearful or afraid of someone? Absolutely. When they are fearful, they are stiff, brace against the pressure they are anticipating and are anything but relaxed and happy. Their whole demeanor exudes fear.
While you think horses are conditioned to do something because they fear consequences down the road, I understand that they are conditioned responses that they have been skillfully taught to do. This is completely different than the fear response.
The more skill a trainer has, the less force or hard pressure is needed to teach the correct response. Once it has been taught, it only takes occasional small reminders when the horse starts responding at a lower level of compliance than it is capable of doing. Some horses require little or no reminders. Some horse have less natural 'push back' or 'resistance' than others. This is determined by background and breeding. We have specifically bred for 'good minded' horses that have 'trainable' attitudes along with specific athletic attributes and abilities.
I like to refer to good training as just 'opening the right door and LETTING the horse go through it'. The good trainer just closes all other doors and lets the horse do the thing that they have made easy (or possible). This is world away from beating or knocking a horse through the right door. If you can't understand that difference, you are never going to get a horse trained to do anything but be a companion animal. Until a person fully understands this difference, their horses are not going to do anything useful, much less competitive.
When I look at the avatar photo of Allison riding the big gray horse over a 5 foot jump, I do not see a fearful horse that thinks it is going to be beaten if it does not jump the jump. I see a horse that has been taught to perform a difficult athletic endeavor.
I am waiting for someone to explain to me how this could get done with a clicker or a treat? Anyone? I think it is the result of just plain good training techniques.