As there are no more auctions
What are you talking about? The US feds still have 90-100k BTC to sell. Plus, MtGox's 200k BTC may be liquidated.
Not that this has much to do with Bitstamp's current need. My guess is they already had a good chunk of BTC by the side themselves. I think Pantera holds Bitcoin as well, and they have the means and experience to acquire larger sums of BTC on the OTC market.