"And because the US government is the only source of dollars"

this is I guess technically true but operationally, the way many dollars are created is wildly out of the control of the treasury. Consider what's confusingly referred to as the "eurodollar."

It's a massive pool of dollars ($13+ trillion!) outside of the control of the US treasury. This pool earns interest in foreign accounts. Deposits created in eurodollar accounts have their own impacts and multiplier effects, just as they do in American banks.

Of course the banks taking these accounts are all a part of the global banking system that the Treasury is a part of - but they don't control much in the eurodollar market, much to their chagrin.

These eurodollars are also of course free to flow into American accounts and assets, or anywhere else for that matter. Eurodollar markets expand and operate with the full blessing of the Treasury, which brings up the "technical" part of saying that the Treasury is the only source of dollars.

When a eurodollar bank deposit is created, the Fed/Treasury have very little oversight on how that overseas bank treats the deposit, how many more eurodollars it can lend out based on fractional lending, or how it's all accounted for.

Much of Fed policy is based on jiggering overnight rates to encourage/discourage certain types of American bank behavior. The Fed has no such lever in the eurodollar market. The treasury does not control how many eurodollar units are created either.

It's effectively a big grey market that means the claim that the US govt is the only origin of dollars is not very true.