As stated, a horse is only as good as his training. I have hopped on stallions who will dutifully go around the arena and through the fields in, around and yes even behind mares. Heck I even ended up taking care of an 18hh young stud at a horse show because the owner had too many horses to take care of. The thing followed all 5'3" of me around like a puppy dog on walks.
I figure, if the stud is so hard to train you can't show it for fear of it misbehaving - why is it a stallion and who the heck is breeding to it?!?