There are all kinds of trainers and ways to train horses.
I see some of those in the videos that are, what is called here, “stealing a ride”, getting on a horse that is not prepared to understand a rider on board and getting it going and hoping he won’t act past what the rider can handle until it gets it going on enough to be ridden right then, then hopefully next time the horse won’t act up as much and eventually it will just put up with a rider.
Today, most trainers work with the horse to help it relax and learn to stand there and accept someone around it and strange ways that person does things and then you finally get on, when the horse is not showing such extreme resistances, where you know it is going to take off running and bucking.
Any way you go about it, the horses will eventually learn.
That getting on and riding thru horse’s resistances is the way cowboys here used to break colts, get on and rush them on so they can’t buck too hard and let them run off until they can start getting some control.
Rinse and repeat enough so the horse finally figures it all out.
Today’s colt starting programs and even the more rushed Road to the Horse type competitions show a whole different picture, where some explain to horses what they are doing so there is minimal resistances, “fight”, brought out in the colts.
The trainers with the more refined skills are like watching paint dry, they can make it look easy, no fireworks, horses learning right along.
Here is an old picture from 1910, I think, called “first lesson”, horse tied down and ready to be let up and someone climb on board and “ride the storm”, generally hazed on by another cowboy on a broke horse.
Some cowboys were very good at that, hired by ranches to come put the first rides on their colts, that then the regular cowboys would take on, once the worst, initial resistances were overcome: