Is this a terrrible play or am I a big dummy?

[KushielsDart]

OK, I just finished a $200 sit n go tourney at partypoker during which what I consider to be a truly obtuse play elevated me to the money round. After lecturing the guy on how foolish his play was (even though it helped me greatly), he suggested I post the scenario on this site. So here it is:

4 players left in a $200 single table sit n go
Me - Button - 1100 chips
Small Blind - 3700 chips
Big Blind - 2700 chips
Other Guy Not Involved - 2500 chips

I go all in from the button with AJ. Blinds are 150/300 I think, maybe 100/200... Small Blind smooth calls and then wonder of wonders, Big Blind pushes all-in. After much deliberation and cursing, the Small Blind folds. That's when I see my AJ is up against AK. Board comes out as 8.9.J.10.J and I suckout and triple up. As it turned out, the Small Blind folded KQ and would've eliminated me. So, instead of being three handed and in the money, it was once again a 4 way battle with one player missing the moolah.

Despite our attempts at telling the Big Blind how foolish his play was, he was adamant that he made the correct play. Although it was a little uncivil for awhile (partly my fault), things got a little friendlier and he suggested I post the scenario here. Your thoughts please?

(Inicidentally, the Small Blind ended up getting eliminated in 4th and I lost heads up to the Big Blind to take 2nd.)