Thank you for finally providing examples.
Before I concede that I was wrong I have two questions that still need answering about them:
1) Did these Indian tribes have property taxes? Since you have claimed that it is necessary to have property taxes in order for people not to own land, then either they did have property taxes, or they did believe in land ownership, or else your premise about property taxes is wrong.
2) Did these Indian tribes ever use any means to exclude people from any parcel of land? Such means would include the existence of any structures, either permanent or movable, which they understood to be any person's or family's exclusive property. Since, if they did have such things, they did, de facto, have land ownership.
Part of my field of study was the political economy of the Southeastern Indians, so you will have to take my imperfect word on it and wait for references and further reading.
The Indian societies were not "perfect" though they used land well. Their societies went through several transitions form extended family kin group band, to free tribes, then to consolidated city-states, then post DeSoto demographic collapse, back to free tribes, so there is no perfect "noble savage" era in the southeast so to speak, but that does not invalidate their claim and right to the land. When they were in the Mississippian phase of paramount chiefdom rule, "tributes" were expected from people and the petty under-chiefdoms, but in general land was shared and was for the most part land use and production relationships could be compared to European feudalism then in later period more like that of the "free-state" Iceland. After this period and into the historic post contact period, tribes utilize a mixed form or property. The people had their own small home plots and small private gardens but they also shared common land to augment the common food supply. Strength in sustainable numbers helped them mutually survive and protect their way of life from future paramount rule. Hunting land was shared but for the most part tribes remained apart and were territorial.
To answer your questions, the Southeastern Indians had a mixed approach to "ownership" of small plots, and personal belongings, yet still shared the land proper. They didn't exclude members of their own tribe, but recognized constriction zones where unofficial borders existed between "territories".
We can't recreate that tribal territorialism but what we can do is borrow from the example of small private use and local group shared resources.
The larger issue I see coming out of the bigger framework of materialism is the issue of land ownership. Theft, trickery, usury and violence was used to wrest this land from the people that were pre-existing. We cannot be vulgar about "ownership" rights now unless we want to embrace the violence and long long history of our kind that got us here. We cannot pay for the sins of our fathers, but we can "check" how we think about legacy and reform how we think about using land. Private ownership is fine in the truly useful subsistence sense, but we have the opportunity to build the notion of the co-op and base land tax based on the notion that a dirty plant takes land away from everyone else and devalues its use. So the plant then is paying everyone else for the right to use it and not just paying some bank financed goon who happened to know the law of usury and state privilege to strong arm everyone off the land.
To make things simpler, large corporations campuses can be charged a land tax which then gets paid out not to the state but to the local organization of people. Land taxes should also be considered for individuals who buy a large amount (20+ acres?) of land and never add use to it while excluding all others.
On the other hand, if your plot just has room for a house and a garden and some power generating and a family size coop of hens, you get off property tax free.
We may not have the answers but the discussion is important because it challenges us to think about the history of land and why it is not a fair comparison for a commodity that someone makes, with possible exceptions to those who truly rescue barren zones and create something fertile.