You take chances getting on a horse,in a car, on a 4wheeler, or out of bed. It's an unsafe world.
"Basically untrained saddle horses"? Outfitters/guides want to insure a clients safety as much as the client. One accident + one good lawyer can put a guy out of business.
A buckoff netted me $15K worth of hospital costs, caused by a dumb move on my part. But I still rather ride than walk.