I just did a brief search on the book and some threads that discussed it and the concept of separation value. Looks like the book's philosophy goes beyond just stats, which obviously makes sense, since stats are simply indicators of other golfing skills like green reading, strategy, etc. etc. and There's obviously more to golf that just stats.
Regarding seperation value, as I understand it, is basically saying the same things that I said regarding correlation to scoring. Higher separation value = higher correlation to scoring. If you're going to work on anything and have limited time, why not work on the one's that have the best bang for your buck. Again, makes sense and that's what I said above.
What I'd like to know, however, is who did the statistical work to determine the separation value of the various stats in the book. Did they do it themselves or did they piggyback on the work of Brodie? Some stats agree with Brodie that the long game is a key differentiator between low and high handicappers, but some of the putting ranges that have high value differ from what I've read elsewhere.
At the end of the day, I think everyone is saying the same thing. Traditional like FIR, U/D, Putts are not that helpful. GIR is much better, but I maintain again, it is not granular enough and doesn't isolate the specific golfing skills required to make it happen. It just doesn't work for me and I prefer to break it down into its specific components separately (i.e. driving and approach shots). Again, that's just my thoughts and preference.