As Herbert has pointed out the 'downswing' begins when the golfer begins it. With Hogan the downswing begins with the lower body. From your statements it seems that the author to whom you refer is talking about the point at which the club starts down. By that point Hogan (and Moe and all tour pros I've examined) have moved their weight to their lead foot.
So as a practical matter your weight needs to come off of your lead foot and then move back to it as your first move in the downswing (and considerably before the club begins the downswing). That is what Hogan does and what Bertholy teaches.