We have analyzed the rearing in hand. It looks like the way Chazot controls his balance when he is at the higher point, is by pushing all his body forward through a small jump. If you look at the hind legs, they are too far forward to carry him. He should then fall backward. His technique is to control balance propelling his body forward through a jump. The interesting point is that he no longer even thinks to rear when he is under  the saddle. When he is mischievous, he bounces forward keeping the neck low. My guess is that the excitement of being into a new place triggered old memories. The lesson is that a horse never fully erases bad memories. Interestingly, the Courbette practiced at the Spanish Riding School is performed through the same idea. The horse is supposed to execute three jumps forward on his rear legs. The Courbette executed at Saumur is more like a rearing. The rider is supposed to stay perpendicular to the horse. Jean Luc