In my case the story was definitely believable when I was younger. My grandmother and one of her sisters were orphaned and sent to a workhorse because my great grandparents could not afford them. I used to think my grandmother did not know her parents but using ancestry.com my mom connected with someone who she thought was simply a family friend growing up but turned out to be her cousin from her aunt who was not orphaned. Going through my ancestry, there is almost certainly nobody who is native. Grandma may have been a little nuts (one of the caregivers beat her do bad that she lost an eye so being a little nutty is fairly understandable).
Good point on few data points for native Americans. Many of them stay the fuck away from DNA testing nowadays so I don’t see that changing anytime soon.