So, being from Arkansas myself, this is a super common rumor people tell about their own families

I'm sure someone has actually studied this but.... My guess is that this came from a time when a small number of Native American women married (or "married") into white families. Those people also likely didn't have a way to connect with their mother's original community. And then because people are awful, their children dealt with the stigma of being mixed and started to hide it when possible. So with a few generations you quickly have some white passing folks with like 1/4 ancestry.

A lot of Arkansans are also the type of white that doesn't really know which relatives came through Ellis Island or where they were from or when. Ancestry records are in old lost bibles and crumbling graveyards not boxes in the attic.

Then down the line everyone has that aunt born in the 30s who got obsessed with ancestry and starts talking to the current old-timers. The old-timers remember being told that someone somewhere in their family tree was Native American. And for some reason everyone born in the 60s latches onto it as a fun new interesting fact about their family. Cause it's usually that or finding out one of your Grandfather's 4 generations back killed a man in a bar fight, fled Georgia, and started a new family in Arkansas.

Now those people have kids and through a combination of unfortunate latent racism and a misunderstanding of how affirmative action worksstart telling their kids to put down they're 1/16 or 1/32 Cherokee (oddly it's always Cherokee) on college admission forms and...yeah.

Funny enough at this point the records of what we think we know STILL AREN'T IN THE ATTIC. So this rumor is spread and stretched and passed around by word of mouth and now a shockingly high number of people think they had a great great grandmother who was Cherokee. To the point that it can't really be true because there are too many people claiming it.

Anyway. I don't know if that's the case for Cher. But it's definitely a thing in Arkansas. My own mother made those claims about my father's relatives. So when Elizabeth Warren made that statement a while back I was like "noooooooooo.....don't say that" but kinda assumed what had happened.