Does that then mean "half halt on the outside rein along with the inside leg"? I've always been taught "steady contact on the outside rein and half halt on the inside rein" (with inside leg on the girth)... So that's all wrong?
People will teach the "half halt" in many ways and in theory you can half halt anyway you wish. Problems will show up later in riding when the aids become more complicated and you will have to change everything you have been taught because they will no longer "get you by".
Just as a canter aid using the outside leg back will have you wringing your hands in frustration when you have to teach the horse to trot half pass by using..guess what...the outside leg back.
Look at the half halt as an adjustment to ANY side of the horse that needs it.