I agree with you, but to be a bit nit-picky; the head can't move anywhere by itself. Pulling the head out, or it's bad movement of any kind; is caused by several things. Mostly the head pulls out because the hitter straightens up their spine, taking it out of tilt. Or, they may straighten the back leg, or both legs. Keeping the front shoulder in, doesn't guarantee that the head will stay in. The head moves due to other body actions being incorrect.
Typically when you get nit-picky I learn something useful about how the human body works