You are leaving out the single most important element of this whole mess: Eurodollars. There are banks outside of the US that take “real” US dollars and multiply them through fractional reserve lending but totally outside of the Federal Reserve System. When the financial crisis of 2008 hit, everyone “discovered” that Eurodollar liabilities were so entangled with real USD liabilities that pulling them apart would be impossible without completely shutting down global trade and finance for an extended period of time. So, the Fed just temporarily gave access to its liquidity for foreign institutions outside of the FRS to keep things running.

Anyways, my point is that Eurodollars can be created, passed around among foreign entities, and destroyed without ever necessarily touching the US flow of funds.