I read the S&T stuff and what they say "others" teach isn't always what they do. For example they think everyone teaches an actual pulling motion across the chest rather and than a fixed upper arm. Well, some do - Stokely does, but he doesn't do it IMO. So probably what others think S&T teaches has some gaps too.
I think maybe there are 7 or 8 schools of thought on rotation.
1. Rotation is caused by a force applied by the trail foot perpendicular to the direction of throw.
2. Rotation is caused by a force applied by the plant foot perpendicular to the direction of throw.
3. Rotation is caused by a force applied by either foot that moves the mass of the body parallel to the direction of throw, and the brace is slightly off center line, so when the mass of body hits the brace it is forced to rotate.
Now multiply these by two: The case where you rotate on purpose, vs the case where you focus on something else and it happens anyway. Stokely is very clear in his clinics: as long as you wait to pull until the plant leg is down, everything else takes care of itself. I asked him about nose up, and he said just don't pull until you land. So now we're up to 6.
7. Rotation is a deliberate twist of the hips unconnected to feet. This I think is the BW S&T idea, but it's also the 3X pitching idea.