This is how I remember the whole scenario. Pardon me for writing a very long post.
There were around 28 players left. I had a healthy stack of about 25,000 to 26,000. Blinds were 500/1000 with 100 ante. People were starting to tighten up as we were approaching the bubble. I was in middle position with AA. I raised to 3500. Everybody folded and I showed my aces. Ariel saw the aces and commented that if I had limped, he would have gone all-in and he would've been in trouble. I replied that if I had limped and he had gone all-in, I probably would've folded my aces as I would be risking too much of my chips as he almost the same amount of chips as me. Besides, if I did limp, I would only have 1000 invested and I didn't think it was worth it.
An orbit later with the blind still at 500/1000, I got AA again. I was again in middle position and I raised it again to 3500. Ariel was in late position pre-flop (button or SB, I can't remember) and he raised all-in. I had around 27,000 to 28,000 and I had him covered by a little more than 1000. I tanked.
My initial thought was he had KK or QQ. I didn't want to go against those. He could have low or middle pockets but with the cards that I've been advertising, I doubt that he'd re-raise against me with those cards. He could have nothing because I said that if he'd push all-in that I'd fold even AA. There's a chance that he has Ax but that's not too probable. And there's a smaller chance that he has AA as well. I decided that he has big pockets and I don't want to be chasing an ace if he hit his trips on the flop and be busted out with only a few people left.
I said "fold" and I showed my AA. I never thought I would ever say that I folded AA pre-flop, but I did. Ariel was a sport and he showed his AA. We both had the same cards and he won the hand without contest.
If I knew that he also had AA, I would've called in a heartbeat. Sklansky said that "Every time you play a hand differently from the way you would have played it if you could see all your opponents' cards, they gain." Does this mean that since I would've played it differently, I actually lost?
Mathematically however, I really had way too much to lose if I had called. All 21 winners would get the same seat which has the same value. I wouldn't need to win 1st place; I just need to outlast 7 people. With my stack, it would be easy for me to do that. My stack wasn't enough to guarantee a seat because the blinds are going to increase but it won't be hard. With the bigger picture in mind, my decision can be seen as sound.
But since there's math involved, there's nothing better than AA and if I won't call with AA, what else would I call with? AA can play against any hand and it'll still be a favorite.
The argument can go both ways and there may not be a right or wrong in this particular case. But I think that just by thinking about it this much shows that my game has matured. I also don't have any reservations about my decision and I'd probably do it again in the same scenario. I won the seat and I think that it made folding aces the right decision for me.