My assertion that they own the land is derived from the actions you describe as having been made by the Native Americans. If someone makes a path, by cutting down branches and bushes, that leads to an open field of buffalo, that someone has homesteaded that stretch of land that is the path. If that someone uses that open field to hunt, then that someone has homesteaded that open field, although he may need to put more labor into the open field. And if an unowned buffalo happens to roam onto that open field, then the someone has the right to hunt that buffalo on his land. However, my problem wih your scenarios is they are vague, and I think that a real-world example would have a more detail in it.
Walter Block is good on this subject. If you want your questions answered, I suggest you consult Block’s writings.