Just to satisfy my own curiosity, I whipped up the below chart of the 24 seasons in which a position player has put up 10.5+ rWAR since 1900 and how they fared in the MVP voting. Mike Trout is just the third player to put up that much rWAR but lose in an MVP vote. In five of the seasons, there were no MVP awards. And three times Babe Ruth had a 10.5+ rWAR season but was ineligible to win the MVP thanks to a bizarre rule at the time that players could only win one MVP award in their career.
Interesting that Willie Mays's 1964 is valued the same as Trout's 2012 and Mays finished all the way down at sixth in the voting. Obviously WAR wasn't a thing in 1964, but Mays did lead the NL with 47 homers. His 16th place finish in batting average may have done him in. Ken Boyer took the prize with a pedestrian-for-an-MVP 5.8 rWAR.
Rogers Hornsby's 12.0 rWAR in 1924 is the biggest rWAR season to lose an MVP vote. Hornsby hit .424/.507/.696 with a 222 OPS+, but he did lose the MVP to Dazzy Vance's historically great rWAR season of his own. Vance had a 2.16 ERA (174 ERA+) and 262 strikeouts, a total that almost doubled the second place finisher's strikeout tally.
So, if rWAR was the only factor—and I, like everyone else in the world, don't think it should be—Mays not winning the MVP in 1964 may have been the biggest miss among these 24 seasons. Trout losing in 2012 would be the second.