"Can someone provide me with a categorically correct theory of the swing that isn't cloaked in controversy?" Probably not,since there are so many different opinions on whats important in the golf swing.
To me, the most important part of the swing is getting to the top of the swing in a position that allows the club head to return to ball in a correct impact position. A golfer's impact position tells the ball where to go.
Best tip I ever received was to swing the club to right field, during the down swing, into the ball. This assuming my body alignment was on a line towards center field. That one tip improved my ball striking to where, once I got it ingrained into my swing, I was saving between 7-10 strokes a round. It got me into the high 70 rounds.
The most proficient sport I ever played was baseball, and using baseball terminology to improve my down swing was easier to understand. In fact another baseball description (term) was to swing at the golf ball like I would a base ball pitch, that was low, and out side.