This is like saying you can't lend out a dollar bill you don't have. It's strictly true, but doesn't accurately represent how the banking system work. The $1,000 dollars in my Charles Schwab account don't correspond to 1,000 physical dollar bills somewhere. They are simply a number in a database somewhere. When I go and withdraw that money, I get back a random selection of $1 bills that other people have deposited.
A bitcoin bank would work the same way. You deposit bitcoins by sending them to the banks wallet. They put a number in a database saying that you have 20 bitcoins in your account. If you then withdraw it, you will get a random selection of bitcoins they have in their wallet.