No. it actually shows that WAR does exactly what one would hope it would do.
According to the numbers, Stubbs has been a neutral defensive CFer this season thus far. In this offensive down year, an average major league bat has posted .255/.319/.406; OPS=.726 good for a wOBA of .316. So Stubbs' bat has been -6.2 runs below average given his playing time thus far. But given his defense and the position he plays, that essentially makes him a roughly average major league player.
In other words, being one of the best defenders on the field (even if you're just average for your position) while being a tick below average offensively is still a useful thing.
If Stubbs is proof of anything, his season thus far is proof that WAR works very well.