We have been de-sensitising horses for thousands of years. It is not a USA natural horsemanship invention. Go back a thousand years or so and look at the Chinese horsemen and the arabs and the horsemen of outer mongolia, the Romans (what did they ever do for us?) LOL. I am sure native americans were using the same techniques too before the europeans 'invaded' The New World (USA).
Erm.... Native Americans didn't have horses until the "Europeans invaded the New World."
Equus Caballus is not a native species to the Americas. How do you think they got there?