So, with such overwhelming consensus that I should have called I couldn't resist digging around this hand a bit more and doing some maths. To recap, it is a large $11 MTT (2,500 entrants), top 360 or so get paid, minimum prize is $16 and it's bubble time.
bankroll not an issue.
I reckon my KK are 40% to win (assuming I am against something like Ax, 99, QJ at best, AA in there at worst). If I call and win I have a stack of 24BB, if I fold I am as good as certain to cash. So, what I am effectively facing is a $16 bet at 40% chance to have a stack of 24BB.
Using the Independent Chip Model I reckon that 24BB stack is worth about $60 and I have a 40% chance of winning it; therefore the call is worth $24. Now, folding the KK would guarantee $16, but my small stack is still worth more than this - I am still in with a chance of placing higher than my current last position. As it turns out it is worth close to $20.
So there you go - the call is worth $24 and the fold $20. Clearly the +EV move here is to call, but I don't think it is quite as clear cut as some have suggested. I think my logic here is sound, but I would welcome any comments that can see a flaw in it.