But you have to have the private keys too if I'm using other BTC when I'm sending?
Right. Theoretically, we can spend everyone's coins, but that is true for other services too (even the client JS ones) and it makes very little business sense to do so.
Thanks. I just wasn't sure if it was a shared wallet or not. Are withdrawals guaranteed that the coins don't come from any of your deposit addresses or is it just unlikely?