I wouldn't have to ID you.
Say:
You deposit X BTC.
You open a position for Y BTC/USD. 
BTC/USD goes down a little so your position is only worth (Y-X).
I liquidate your position.
Now mtgox has (Y-X) + X which = Y which is the amount of the loan.

The exchange hasn't lost anything so I don't need to know who you are.