While each maneuver is in and of itself seperate from the next. The back is part of the stop. This is how you get those big stops. The horse is thinking back as it stops. Again watch the video I posted. Watch how the mares back feet are going back before she even comes to a complet stop.
Go and watch people like Shawn Mike Stacy and so on train a horse to stop. It is all about the back up.
Thinking ahead can and does get you into trouble this again is why you change things up. However with the stop it really is one of those places that the horse thinking back is a good thing. Again watch any of the top trainers train the stop. Most will keep saying whoa as they back their horses.