Or they could operate using fractional reserve method, a 90% reserve is still much much better than any banks which only have 10% of client money at hand.
That's not what "fractional reserve" means. For a bank, a loan is an asset - someone owes them money. Banks get into trouble when many loans go bad, as happened when the real estate bubble popped. Or they get into trouble if they have short-term deposits and long term loans, and too many depositors want their money out at once.
That's not Bitstamp's situation. They don't own 30-year mortgages. They have no big illiquid assets they can sell off. They have nothing except their customer balances, and, according to their financial statement filed with Companies House, a few hundred thousand in paid-in capital.
Bitstamp needs $5 million within days, or they're going into bankruptcy.
It is the same, although banks claim that they have this and that asset, when they suddenly need money, those loans can not come back in one night or one month. In fact 90% of the deposit money are just sitting in the bank's account without moving, that is the original reason banks loan out those money to earn interest on those dead money
What those coins in bitstamp's cold storage are doing? Collecting dust. They can actually loan out those coins and operate more like a real bank, but without loaning anything out they are much safer than a traditional bank if a large scale of withdraw is happening. For normal bank, if more than 40% of customer are doing withdraw simultaneously, they will run into a liquidity crisis and go broke. But unless more than 80% of bitstamp customer withdraw from bitstamp at the same time, they will be fine (Of course I suppose that they are doing 100% reserve, if they already practice FRB then no one knows how serious the situation is)
BTW, they don't need $5 million, they only need 19000 coins, no big deal for them. But if bitcoin price suddenly rise by 10 times, they might run into problems, just like MTGOX experienced, their initial loss of 200K coins caused by 2011 hack becomes so huge amount of wealth after 2 years that they can never earn it back