But if the exchange had half their USD bank account balances seized and froze half their customers' USD balances the effect would be the same -- freaked-out people would still rush for the exits by buying BTC, even though tradeable USD on the exchange had suddenly become scarce.
This isn't about supply and demand, it's about final delivery mechanisms during times of crisis. Bitcoin is more final than the fiat currencies used during the last 50 years and quicker to move than the precious metals used during the previous 5,000-odd years.
It's still about supply and demand. The reason why the prices might rise in your example is that the supply of bitcoins (ie. demand for USD) would shrink to almost nothing, while the supply of USD from desperate owners would increase. You have to consider supply *and* demand.