https://www.nationalparkstraveler.org/sites/default/files/at...
It refers to 31 U.S. Code § 5103:
> United States coins and currency (including Federal reserve notes and circulating notes of Federal reserve banks and national banks) are legal tender for all debts, public charges, taxes, and dues. Foreign gold or silver coins are not legal tender for debts.
https://www.law.cornell.edu/uscode/text/31/5103
They argue that the fees at the parks are public charges, not debts. I can't find anything in the US code that provides a definition for "public charge." It may be there and I just haven't found it. It seems likely that there are prior judicial cases that help shine a light on what is and is not a public charge. I hope these folks win.