Sure, I'm not saying that it's reasonable to prosecute the neighbor for the prior act of building on someone else's land (though I'm not sure that's a crime; at worst I expect it'd be a form of trespassing, but would otherwise be a civil matter). I'm just noting the weirdness that the legal status of the property was changed through an initially illegal act.

But I guess on second thought maybe it's not that weird? Like if I buy stolen property from someone, and I have no idea that it's stolen, and the original owner comes along wanting it back, it's actually now legally mine, and I'm under no obligation to give it back.

But that's not exactly the same, because in this case the original owner has been harmed, but making the original owner whole would then harm me (an innocent bystander). In the case of the real property issue, "giving back" the land would only harm the person who "stole" it in the first place.

However! If the original "land thief" were to sell the property to someone else, then you're in the same situation. The new owner bought it in good faith, expecting the fenced-in area to truly belong to them, not knowing that the original property lines were drawn such that some of that property actually should belong to the neighbor. So then acknowledging the status quo means hurting the neighbor, but transferring the property back means hurting the new owner (an innocent bystander). At least in this case, the new owner could perhaps sue the old owner for misrepresenting the size of the land.

That's again not accurate at all. If you buy stolen property & the original owner makes a claim to it within the statute of limitations, that property is returned to the original owner.

Anyway, as many others have noted, the problem isn't that the statute of limitations hadn't expired. What was actually happening was that the government was regularly breaking the current treaty that was in force. The ruling was that the government has to follow the law or change it but it can't just apply it however it wants.

I think it's interesting that a debate about the impact of adverse possession upon the original land owner has resulted from a SCOTUS decision about a Treaty between the United States and an Indian nation.

On what basis was the rest of Oklahoma not "adversely possessed"?

Reservations aren't property of the tribe or nation, they are areas of federal jurisdiction under a Constitutional reserved power within which the tribe and federal government has certain jurisdictional rights concerning members of the tribe, and where the state is excluded from certain jurisdictional rights it would otherwise have over territory within the state.

I understand statutes of limitations are about blocking prosecution of past infringement, not granting a legal right to continuous infringement.

If the statute of limitations for conversion has expired, you will no longer be able to recover either the chattel or its value from the converter. The analogy to adverse possession or easement by prescription in real property should be fairly obvious.