Patrick,
You just made Dave's point for him. You said top PGA tour players were consistently great in all phases of the game. That's the difference. There are plenty of low handicaps who are occasionally great in some phases of the game, and perhaps pretty consistently crappy in other phases. That's all he's saying.
Hell, put it down to luck, if you like. If a low handicapper has got pretty much the same swing speed as a given tour player then he's capable of hitting the vast majority of shots that tour player is. It may be pure luck that he wants to fade a 3 iron with the ball well above his feet and he does it, and he couldn't reproduce it or even tell you exactly how he did it, but if the ball does the same thing it doesn't matter. The ball doesn't know the handicap of the player who struck it, it just knows clubhead speed, angle, swing path and angle of attack for a less than one inch impact area. Whether the clubhead is propelled there by Ernie Els' swing, Jim Furyk's swing, or my swing is immaterial for that one shot. I think this argument is going back to the 1 in 20, 1 in 100, 1 in 1000 discussion from a few months back...
As for what I'd do if I were invited to Augusta. I'd play the Master's tees if at all possible, and if I had any sort of location where I thought I had any chance whatsoever (even if the result was down to dumb luck rather than skill) of putting it on either of those greens after my drive, I'd do it. What's more, if my host was in a generous mood and there was no one behind us, and my drive on 13 was substandard and then again on 15, I'd ask to hit a few more drives on 15 until I came up with one that I could have some sort of a go at, then try some from there. I'd feel unfulfilled if I didn't get to give it a go on at least one of those holes, wouldn't matter if my shot at it wasn't in regulation play.
This is just required at Augusta in my mind, just like going for the green is required on #16 CPC, even if my one shot ever there turns out to be into a 40 mph wind. Other requirements include challenging the Road Bunker with your second from wherever you are, playing over Strath to that difficult pin on the edge of the false front on Eden, challenging a back left pin on any Dye cape hole (#18 Harbour Town, etc.)
If you can play a course only once, who gives a crap about what score you end up with? If you get to play it a second time, then maybe you can worry about score, or catch up on the requirements you missed from the first time. Its amazing how people in GCA talk about the "score and pencil" mentality then are quick to put caveats on when they might try for the green in two at ANGC. So you dump your second in the water and take six. I'd rather hear about someone doing that then tell me about what club they used on their layup before their safe pitch away for the pin and conservative lag putt to gain them a par.