That's a fiction.
Bank comes from the Italian banco, because bankers sat on benches and did their money-changing right there. (Niall Ferguson, The Ascent of Money)
Banking was a service needed by the export/import trade, and started (or better, was restarted) in medieval Europe in response to this. (Innumerable histories; pick one) According to Paul Einzig in The History of Foreign Exchange, the first bills of exchange were issued way way back, in Babylonian times. Even then, it had to do with exporting and importing. As of today, international commercial banking is still, by a far and very wide margin, the largest part of the banking business. Foreign exchange is intimately tied in with money market operations in these banks, and the two are interchangeable almost, which is why the operations described by Einzig in A Dynamic Theory of Forward Exchange exist. Without the ability to lend out against goods shipped but for which payment has not yet been received, and to convert those payments into an equivalent amount of currency A from currency B via forward exchange, the entire apparatus of world trade would come to a screeching halt. This almost happened in the fall of 2008, in the middle of the late unpleasantness, as a matter of fact.
This is how the actual world that we all live in works, and has worked in every commercial civilization that has ever existed. No one except the Austrian ideologues thinks otherwise, and the only reason I can think of is that they still have in front of them Charlemagne's monetary system from the Middle Ages.
Charlemagne, of course, used silver rather than gold, gold being too scarce to make practical use of at that time in Europe. I'll bet a silver dollar that little tidbit of info is something you never see out there on those rad-lib sites.