One of the times a horse reared up and fell over backwards on me was when I was riding an unbroken horse.
I do still ride bareback, I've always done it and it just seems right for me. As a kid I jumped bareback, ran barrels bareback and other dumb stuff. My worst accidents were when I had a saddle on. I am, however, very careful of the horses I now ride. They have to be very reliable to be a bareback mount. The horse I ride the most now is a paint and you could set him on fire and he wouldn't do anything.
LOL! Never heard that one before. My mare's pretty bombproof, a huge industrial diesel air compresser once cut on within ten yards of her and she didn't even turn a hair (I jumped a mile). The only times she's shied with me are when some kids were giving each other wheelbarrow rides and shrieking and popped out from behind some trees, and when some guys were unloading oil drums from a truck and let one roll away down a hill. She has the grace to plunge straight forward, though, so I didn't come off either time.