And then when depositors withdrew the money proper, bye-bye bank.
No, the bank would collect Charlie and Bob Houses from the default on the 1 BTC. They didn't print money, they created Debt money contracts. They did this with Gold for centurys.
Debt money contracts are bank notes. Good luck getting someone to accept a Bitcoin bank note, when it offers no more convenience over using BTC. People wouldn't trust it.
Think a loan, a promise to pay BTC in this amount of time. Its not money, but it is DEBT. They did not print anything but created 1 BTC worth of debt through the loan.
Whoever purchases the debt (you're referring to trading debt) assume the risk of the loan defaulting. You couldn't use these contracts to purchase goods. Only to cash in on the debtor.