With the tribes government, politics and could also be their traditions. Some tribes have given up their DNA in the past and it was misused. They filed law suits and won. The Nations in general are protective of their enrolled members. Some however may test on their own but still may not want to share info. They dont just want people coming out of the blue trying to enroll just because one may find record of AI ancestors. Rule is if you did not stay with your tribe you lost citizenship to the tribe.
You can do a stripped down tree but it still creates a trail to the living even though the living stays private. It gives the rights to ancestry to sell your info if you make your info public in their system. Also if you did not read their DNA consent they are using the DNA testers for a study. You had the chance to opt out by not checking the consent form when you registered your DNA kit which my family did opt out. That consent form is very sketchy about what they are using your DNA in their study for. It does mention medical and other things. If you did not opt out of the study you can email them to opt out now but it wont stop what they already might have done with your DNA in their study