Mt.Gox needs to calm everyone down by signing a message from an address (or multiple addresses) that contain enough bitcoins to prove that they can handle the withdrawals.
If they do not do this, we must assume that they are insolvent and have lost their customers' coins.
Why would that anyone holding a lot of coins need some incomparably small sum from MtGox while he can clearly make more selling it before the meltdown on other exchanges?
By propping up MtGox he'd be keeping the value of his Bitcoins up. If MtGox fails, there'll be a huge dip in the price of BTC across all the exchanges.
I would agree with you, in the context of the fractional reserve system.
But in the case of a cryptocurrency exchange the credits and debits should be more or less equal, minus the trading fees. At least, that's how places like Mt. Gox promote themselves.
It may take longer to get your funds, if there is a "run" on the exchange, because of the flood of transactions into the system and the need to reconcile everything, but that would likely be measured in a few hours extra, not days/weeks.
If they do not do this, we must assume that they are insolvent and have lost their customers' coins.