I'm sure you know when you sway your head, but I'm just a little skeptical that it's because you can sense how much your eyes have moved in their sockes.
It's not the amount of eye movement. It's all the changes in your field of vision, if you move.
Back on point... the more stationary the head, the less things change as you view them. The eyes help in this area.
The good thing about this site is that intelligent people can agree to disagree or find common ground. It doesn't have to become a urinating contest. We know that there are plenty of places to do that.