The government accepts the $20 as a legal way to pay your taxes, or other government fees.

That is true. But if the only way a government owes me something is that it has to accept dollar bills to erase my tax/fee duty, then I think this proves my point - the government does not owe me equivalent of those bills, it only has to accept them for limited set of "services".

"I could go to a store and buy a bottle of expensive wine for that bill. But I wouldn't say the store owes me."

That's a misunderstanding. A $20 bill is the government's liability, not the store's liability. You and a third party are using government liabilities as a currency. Every $20 bill is on the liability side of the central bank's balance sheet. Every entity accepts its own liabilities as a form of payment. Governments issue currency which they then must accept as payment for taxes. Banks issue credit which they then must accept as payment for debt service.

https://www.youtube.com/watch?v=TDL4c8fMODk

Interesting video, but can't help to notice it paints too simple and dandy picture and probably has an agenda behind it. If you read the comments, not everybody believes in this "the government created the money so there is no problem in creating some more" idea. In principle yes, the government has that power. But in practice, this is being prevented by powerful people in and out of government and only gets a pass in special cases (like saving the big banks yes, funding public healthcare no).

The answer is gold. Your $20 is worth a certain amount of gold, and that is what the government owes you. $20 in gold. These days you'd be hard pressed to get the government to give you gold, of course, but that is the answer to your question.

As an example, British pound notes have the wording "I promise to pay the bearer on demand the sum of five [ten/twenty/fifty] pounds", which dates back to a time when you could actually exchange the notes themselves for gold.

This used to be more literally true: https://en.m.wikipedia.org/wiki/Silver_certificate_(United_S...

Not quite... https://www.history.com/this-day-in-history/fdr-takes-united...