You can not lend out 1,000btc, just because you got 100BTC in your wallet.
Sure you can! Just not on-chain. Just like a bank can lend out a million dollars without having a single physical dollar in the entire building. As long as the dollars (or Bitcoins) only exist on their own accounting system, they can pull it off.
If you try to withdraw a million dollars, the bank won't let you. The same will happen to Bitcoin if they get their way.
I'm not giving them my coins, nor my keys 