OK this is getting dangerous - a pitching guy wallowing with the hitters. I am going to go with PTOF as far as explainations of what is going on. I can add some physics and see if it makes sense.
The guy who taught my son to hit always said.
1. Hit off a firm front foot.
2. Hips lead the swing and create power.
Now if all of this is true and PTOF is correct then the physics would work as follows:
Looking down from above on a right handed hitter the swing MUST be initiated with the rear foot which would drive the right front hip to accelerate, this is the only way to initiate the swing as this is the only place the force can be applied to get the hip moving. The left front hip then is rotating back against the front foot which has to be pushing back otherwise the whole body goes into forward motion. The forces would have to be equal and opposite to generate rotation and if one is less than the other then the body begins to move in the direction of the lesser force. (if you assume a symetrical body)
Obviously there is all kinds of other stuff going on but the basic physics have to be as I have described as there is no other way to get the hips moving.