Can I fold AA preflop? Yes. Should I? Usually not. Are there EVER times where folding AA preflop is justified? Yes. The best example I can think of is the rare situation of you playing a satellite and have enough chips to quality if you just fold every hand. There is no real incentive to play anything in this situation. If the rare case you are dealt AA here and the action gets going, you may be justified in folding this hand preflop.
Other situations to potentially fold AA preflop is when there are outside factors to the hand such as this famous hand on the loose cannon show where the amateur player was dealt AA and CORRECTLY folded preflop! What justifies this play is that he had just made a substantial amount of money and just had a few more hands left to play before he could "cash out" of the show session.
Objectively, AA is the best hand preflop, so if it wasn't for outside factors, then you should be playing it every time (if you fold, then what is good enough to continue with? If nothing, then why play the game at all?) If you are playing to win, then you'll probably always want to play AA, but if you only care about min. cashing or barely moving up the payout ladder, then you might fold to survive slightly longer. However, this isn't usually correct. The "big money" is at the top in large events, so usually you'll want to be shooting for a win. Hand starts at 5:44 in video clip