Couldn´t agree more!
I´m a good example of the second paragraph. Last tournament (72 holes - 6700 yards, par 70, rating 72, fast greens) I lost 20 strokes against a pro.
Drive: 5 (i´m a short hitter)
Putt: 13 (just holed one 15 footer outside 10 feet in 4 rounds)
You could say that i just need to improve my putting to compete on PGA tour.. but no.. That´s my stats on a 6700 yards course. On a 7500 yards course set up for a PGA venue with a rating of 76 my stroke gained Driving and Appr will rocket to the sky, above my poor putting stats.