Personally, I think the goal is to take the slack out of the wrist, which then allows you to control the elbow, which in turns connects you to the shoulder, then the rest of the body. You shouldn't be torquing the wrist as a mechanism to do the throw. Once you connect, you can shift their balance where you want the person to fall.
One of the biggest problems I see are people simply torquing the wrist. It really doesn't do anything, you have to actually effect the elbow-hips, like you say. Its an arm-body throw, you are just using the wrist to get there.