Observing any GOOD athletic "throwing" motion, such as throwing a baseball/football, hitting a tennis ball, a hockey slap shot, the lower body always starts forward before the upper body does. A good golf swing is no different. The lower body movement happening first, helps to retain the trail arm/wrist angles so that when they "release," they do so later and greater power and accuracy result.
In most of us this movement is subconscious and may not be felt, but it does happen. What the Bertholy method does is that it trains you through slow motion and static positions to make the correct motion(s), so that when you swing they happen without any conscious thought. Frequent(thousands) of slow motion repetitions of the correct movements are necessary to master the correct movements.
If we use Moe Norman as the premier example of a correct SA swing, it is very obvious that the body moving forward and the arms dropping down do NOT happen simultaneously. Moe lead leg buckles forward "long" before the arms drop.
Yes, there is a lot of analysis on this site and it is interesting, however, no one is suggesting that you have to think about all of the parts of the swing when you swing. I may have a detailed understanding of all of the various parts of my car, but when I drive it, I just "aim and fire."
Even JK says that the problem is not "paralysis by analysis" but, "paralysis by INCORRECT analysis."