Yes, Native Americans have private property rights.
You're doing what the Left often does with Western countries. You're applying 21st century morals to 17th - 19th century activities and ignoring all context. Of course, we forced Native Americans off of land. Of course, we had legalized slavery for hundreds of years. Of course, we mistreated ethnic and religious minorities. And yes, other Westernized countries have done other things we'd judge harshly today. However, what you ignore is that what the West did wasn't harsh or morally questionable by global standards at the time. When other societies just storm into other lands and torture or starve everybody to death, Indian reservations don't look so bad. When African tribes were literally butchering and eating each other or getting slaughtered by Islamic conquerors from the Arab world, British colonialism didn't look so bad. Furthermore, part of Western civilization is self-reflection. We can look back on slavery and other past bad acts, see the immorality of them, and at least make some effort to make things right.
Genocide and slavery are considered remarkable acts of brutality today. Not long ago, they were commonplace and routine, because most civilizations didn't give a crap about nor consider the well-being of anybody but themselves, and plenty of them still don't and still don'tst.