I personally believe that its the way a reining horse is trained that makes it just walk out of an arena on a draped rein after completing a pattern. Obviously temperament and genetics help. But there seems to be a lot of mind games when training a reining horse.
Making the right thing to do easier than the wrong thing - like when I ride I leave sliding until the end, and as soon as I get a good one I get off my horse, that way he associates doing a good slide with stopping work, therefore he WANTS to slide. Same with spins, if the spin goes wrong I ride him out the spin and and make him work in hard circle then spiral it back down to the spin and release my aids, therefore being in the spin is easier than out - its a place he wants to be.
A reining horse has to have a good attitude and a good work ethic. Has to handle going from fast to slow, sliding into a stop from a gallop to standing on a draped rein. I love a well trained reining horse because to me they are true examples of an obedient level headed horse that can be trusted.