Doesn't necessarily have to be a white belt, a purple belt wouldn't want to go to the ground with a black belt either (or in my cases a blue belt against a better blue belt).
And in real life if a fighter knocks someone down, he'll be punching his heart out on the ground while the other guy is covering up. In this game, he'll often just lie on the ground and control while the other guy sweeps or tries sub after sub. Sometimes he'll even jump to the ground, and then he'll just try to get back to his feet.