Banks don't lean from deposits even in the "official" narrative.

A bank that needs to lend money that doesn’t have it's going to use the interbank system in order to get "reserves" from others banks.

The idea is that the causality is inverted. Banks lend and then search for reserves. If you see it this way, you realize that there is not constrains in how much money they can lend (except how expensive is to find reserves).

Try this (maybe more clear than the other): http://bilbo.economicoutlook.net/blog/?p=14620