Zone #1 (Pivot) must be mastered before Zone #3 (Hands). Zone #3 can never be better than Zone #1. So don't go "ooh, xyz is a rubbish teacher because he is always talking about pivot this and pivot that." He may merely be teaching the proper use of your Pivot before you can progress onto the Hands Zone.
The Golfing Machine is about Hand Controlled Pivot, not the other way round. Homer said the Pivot Controlled Hands procedure is so inferior that it's not even worth considering, except during transitional periods for the player.
Pivot Controlled Hands assigns to Physics precedence over Geometry -- Force dictating alignments. Which obviously reduces precision. But the Pivot may be educated to produce geometric Hand and Club alignments and relationships with some degree of precision which would definitely improve control.
In Swinging, Horizontal Hinging is naturally produced if centrifugal force remains unhampered. This is the 'physics dictating geometry' aspect some people talk about. More specifically, it's Clubface geometry. However, the Educated Hand and the Right Forearm is needed to maintain the On Plane Sweetspot and hence Clubhead and Clubshaft Geometry.
The hands are always aiming, sensing (via Pressure Points) and relaying information to and from the club. If they are educated, they dictate how the pivot should move by themselves.
Hands Controlled Pivot doesn't mean hitting the balls with your hand so the pivot doesn't do any work. The Pivot still acts as a massive rotor transfering momentum to the club. The difference is merely in what you monitor.