And your argument comes down to completely statistics and I happen to be one to believe that there's more to baseball than statistics. Even Fangraphs has a statistic for "clutch", something that's been discussed ad nauseum here, and I believe that some players perform better in clutch situations than others do - but according to some it's not statistically provable. But that doesn't stop me from believing it or Fangraphs from calculating it.
I DO completely get what WAR is attempting to measure and I believe that on the whole it's fine. It's just that like any other "hard number" there are exceptions to it - extenuating circumstances, if you will - that contribute to the statistic that are unquantifiable. I've been saying for years that I wish there were some quick and easy (and understandable) way to compare one player's total worth to another, but I still don't see it happening. There are too many variables and unquantifiable things that go into human beings playing baseball.
IMHO WAR is great for historical data and for predicting what a player might do over an entire season but it's essentially worthless (that may be a bit of hyperbole ) when it comes to predicting what a player will do in any AB or in any ball hit to him. Those things are the result of the makeup of the player.
(Example: Jose Iglesias has all the skills in the world as a SS but I've read that his problem is focus. And in a totally unrelated thing, have you noticed how many players when interviewed seem to have some of the ADHD thing going on?