The problem with clever marketing is that it can make it more difficult to see how a behaviour was trained.
For example, you could train your horse to trot when you click your fingers. You could do this with positive reinforcement, getting the behaviour through shaping and putting it on cue.
You could also do it via Negative Reinforcement and Positive Punishment by whipping a horse after you click. The click becomes the predictor that a whip is coming unless they move. For this to work, you have to start by using the whip and can later fade it out, because the threat of an aversive is still implied by the cue. You may even need to bring back the whip periodically to keep the behaviour sharp. But the end result could look similar to one taught with Positive Reinforcement. The trainer clicks and the horse trots.

Add in a few nice words about how kind and gentle your ‘method’ of training is, and it can become nearly impossible for a layperson to identify that aversives were used when viewing only the final product. It can also cheapen the behavioral opportunities that Positive Reinforcement provides, by referring to training as a ‘method’.
The truth is, if you tried R+ and it didn’t work, then you actually weren’t using R+.
By definition, by science, it WORKS. If the behaviour didn’t increase then Positive Reinforcement didn’t occur. It can’t be written off as not being suitable for all horses because there’s no magical or mythical horse that simply ‘doesn’t suit’ R+.
While training is the study of one, we have to be realistic. Your individual horse will have different food preferences, a different learning history and won’t always react the same as the horse next to it. But at the end of the day, a horse is still a horse. An animal is still an animal.
Things like individual trainers courses and clinics will vary with their success rate. Many horse owners will say they tried XYZ method and it didn’t work ‘for them’.
But in truth, it’s more to do with a fundamental lack of understanding or misunderstanding of how learning occurs.

Of course your horse is special and individual, but they're not exempt from being a horse who learns based on consequences.

Positive Reinforcement is for every animal, every horse.

Written By Madi Holmes of the PPGA Equine Sub-Committee