I was under the impression that the "independent nations" concept implied independence from the states. Naturally as the power in the US has shifted away from the states towards the federal government the autonomy and sovereignty of the tribes has decreased.
https://www.bia.gov/frequently-asked-questions
> Tribes possess all powers of self-government except those relinquished under treaty with the United States, those that Congress has expressly extinguished, and those that federal courts have ruled are subject to existing federal law or are inconsistent with overriding national policies.
That has not changed at all.
It sounds strange, and it kind of is, but in reality life on a reservation in most cases is rough, few options to make a living, lots of substance abuse, tribal politics can be pretty petty and nasty. I lived near a reservation for a while and the first thing you think "oh man they have this nation inside a nation they could do a lot of things" but really life is rough there.