I think the idea is that most people aren't computers processing laws as if they were code; most humans have to primarily go by what they see happening around them in order to decide what is ok. If they see lots of cars going down a road, eventually they assume that it is public property, even if they never check the public records to see if it is. Similarly with lots of other things.

But, crucially to the Supreme Court's majority decision, you have to have a law saying that this is so (for real estate or intellectual property or whatever), for it to be so, and Congress never did that.

https://www.atlasobscura.com/places/standard-oil-gas-station

EDIT: they have one each in 16 states, so not exactly “lone”

Yes, the point is there is a specific law that says this, and it's really not that unreasonable, since precise property boundaries are always ultimately conventional.

I understand the reason why someone might not trust the most local government (municipal, state, federal governments as appropriate) to manage the registry of landownership complete with dates, dimensions, notables features, and owners, but I find it really weird that problem of knowing exactly who owns what is effectively an orphan in the last resort.

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.

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.

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