That's because these are the thresholds used by most universities and financial aid services for grants or scholarships. My great-grandfather was the last one in my family to identify as Native American (Apache and Commanche), but between my mother's ancestral bloodline (Apache, Commanche and Cherokee) and my father's (Nakota and other Sioux), I qualified for programs, even though I'm multiple generations down the line.
All of the ones I've seen, and the only such scholarships I've had, have required proof of tribal enrollment. I've never actually seen these ones that accept 1/16 or 1/32 of arbitrary tribal blood, but I suppose they must exist.
There is actually the opposite problem for many young Native Americans today who have 100% native blood, but not enough from any single nation to qualify for anything.
If frustrates me that so many people say "oh, I have such-and-such percentage of blood, so I could qualify for X if I wanted," because in most cases, my experience has been, no, no you can't. You have to be an enrolled member.
And it also creates problems for natives from smaller nations that aren't federally recognized.
Edit: There are of course those places and programs that will simply take your word for it. But I've never seen one that has its own separate and unique blood quantum requirement distinct from tribal enrollment.
Edit 2: I was wrong. I just did a search and indeed found several scholarships that allowed eligibility by blood quantum in lieu of tribal enrollment. But for all of the ones I found, the required blood quantum was 1/4.
Edit 3: Please forgive me if I am sounding testy. Blood quantum is a touchy subject for me.
Edit 4: I want to explain one reason the misconception bothers me. There is a misconception that there are all of these scholarships and fellowships and federal aid and other money and opportunities out there for anyone with a drop of Native American blood. There is a misconception that there is tons of money out there going to people who are 1/32 or 1/16, and all of these people are just getting a free ride or benefitting for nothing. None of that is true. There
is money out there to support Native Americans in higher education. But it's hard to find people to give it to. It's incredibly hard. Because the students who could use it don't see a version of themselves in college, or in graduate school, or becoming a professional. And when they realize that could be them, they aren't prepared, because the schools and the system have already fail them. So the money goes to no one. I tried to turn down one such scholarship because I already had an NSF fellowship, so I didn't really need it, and I wanted it to go to someone who really needed it. The director of the program looked me in the eye and said if I didn't take it, it wouldn't go to anyone. There was no one else. He told me to take the money, and use it as an opportunity, to do things I could've have otherwise, and go out and show other young natives what they could do if they wanted to do it. So that's what I'm trying to do. I know it was meant with good intentions here. But that's just why it always bothers me so much when I hear people talk about scholarships and blood quantum in a certain way.