I agree most GM's don't use back of the baseball card stats to make decisions.
However, this thread is not asking us to be a GM and decide whom to trade for, or whom to sign. It's asking us who has been more valuable to their team. And for that, a strong argument can be made for back of the baseball card stats.
It really comes down to a difference in philosophy on how to understand the game. If you believe that the game is played one game at a time, and the goal is to score one more run then your opponent in each game, then you value things like RBI's, ERA, batting average, bunts, baserunnimg, fundamentals, etc. these things help you win actual games, one game at a time.
But if believe that the game is about scoring more runs than you give up over a full season, if you believe that the goal of a team is to have the best run difference in the league, than you value advanced stats like wOBA, UZR, XFIP, etc. These evaluate how well a player generates or,prevents runs in general, theoretically, over the course of a full season.
I'm mostly in the former camp, but I understand and respect those in the latter camp. I don't think it has to be an either-or proposition either.