I certainly see your reasoning for the fold here and I find myself folding for the same reasons as well.
But I have been wondering on this sort of problem for a bit now and I'd like to give a couple of arguements for a call/shove (mostly shove) in this spot.
1: JJ is only dominated by QQ-AA, and slightly ahead of AQ, AK. More likely you may be ahead than behind.
2: Being scared to shove with the 4th best hand in the game, so early in a SNG is IMO (and I do this as well, so..) weak. As you stated, it is still early, and you are presented with an oppritunity to stack an opponent and double up, or bust and fire up another game. Very little time invested and good cards to back up the shove.
3: I see more plays like this (from villian) with hands like 66-1010, (maybe even al low as 44) than with AA KK. This is because most players want to play mid pairs for a reise, but they are scared of seeing overs on the flop as well, and therefore raise huge in order to narrow the calling range against them, and still be able to rep a big pair like KK+. Even if everyone folds to the huge overbet, they still get the satisfaction of playing, and winning a pot with their small pair.
4: You have position. If you choose to flat, (which is usually a bad idea because you know the shove is coming on the flop regardless), you have more oppritunity to either get away if you are crushed (but if you flat, you're not folding given the stack/pot ratio) or see a nice dry little flop and gain confidance that you hold the best hand and happily call the shove.
Personally I think #4 is not a great line to take, but I threw it iin there just for the sake of discussion. Like I stated earlier I too have a problem with folding large PP's to a pre-flop overraise early in a SNG because "they might have aces". I realize now that more than likely, they don't. Would you raise half your stack pf with aces? I sure as hell wouldn't. But I could see myself raising that amount with a hand like 99, making it look like I'm so cinfident in my "monster" that I'm going to stack off anyways.
I dunno, what do others think about all this??