What you both are talking about is intention. The handler's intention is everything. If the body language says, "move your hiney", the horse will read that and move his hiney over when the person walks around. If the person's body language says, "stay here, I am just walking around you to check the cinch , or to grab something from the ground behind you , or .. ." the horse will know that there is no "push" in the riders' body, so will stand put.
In that video, I found it pretty hard to detect the change of intention in the handler's body, but apparently, the horse can. I thought her body had a lot of "push" in it, all the time, even when she walked up to reward the hrose, but the horse can tell the difference.\
There is one problem with "chasing " the hind around, and that is that the horse learns to plant his front feet, and spin the hind around behind him. And, the horse can sometimes get so used to doing this, that they do become hard to move around , without causing them to spin around their front legs, like they are trying to screw them into the ground. And they will try to keep you in one eye only, such as their left eye.
More than just having the hrose swing his hind over, you might want the horse to first look over at your and maybe bend his neck around the corner a bit , so that when you do to ask the hind to move over, he is doing it softley bent, instead of swinging like a gate on a hinge, heavy on the forehand.
To guage if a horse is really backing up well, watch to see that the diagonal pairs lift and move together . The horse will really have to be rocked back and balanced to do this. There is not reason why a person cannot do this with a lead attached.