Here's the Fangraphs WAR data for these two:
Code:
Batting BaseRunning Fielding Replacement Positional RAR WAR
Braun: 52.4 3.3 4.0 20.9 -6.5 74.1 7.8
Posey: 44.2 -4.1 2.6 19.2 6.0 67.8 7.1
I don't see a 2 WAR adjustment in there. I do see the 12.5 run difference in the positional column, which is what I assume you're referring to.
Regarding catcher defense, here's how Fangraphs handles it:
So that notably leaves out pitch framing. I don't know how Posey rates there. I saw one article that had him at +8 runs in 2010, but who knows the accuracy of those ratings or their consistency year-to-year.
Both Fangraphs and B-R have Braun & McCutchen ahead of Posey and have Posey and Wright more or less tied. But the difference is less than 1 win. I'm basically giving Posey extra credit for the value of catching I think WAR misses, but think there's certain a defensible argument for any of these guys -- certainly more so than the AL race.
_____
On a separate note, let's stop treating WAR like it's another stat alongside things like Homers and RBI. The value of the other things is captured in WAR. You can choose to use those things instead of WAR if you think WAR is just bad math. You can make your own version of WAR that values things differently. Or you can supplement WAR with things it doesn't include, like leadership, chemistry or special accomplishments. But adding components of WAR to WAR is silly. There's no logical argument that says, well, they're equal in WAR but this guy has more HR or that guy has more SB. Those are already in there; there's no reason to count it twice. It would be like saying that 1+2+3+4 > 0+0+5+5 because 2 is greater than 0. It just doesn't make sense.