Being as I am related to a Choctaw medicine woman named Mourning Tree Frasier, who was the daughter of an Indian woman and a French voyager, who lived between 1810 and 1867, I can relate to this. Not me nor any of my immediate family have ever claimed a dime or an acre or anything else because of related to this ancestor. Mourning Tree is another word for Willow. She was the only person with any medical skills on the Ft Washita reservation, which was closed in 1858. She married a 5th great grandparent of mine named Lemuel Gooding, who was the sutler and a Methodist minister to the reservation. Both his wife and Mourning Tree's spouses died in an epidemic in the early 1850's. I have in my possession the account books of the sutler's store. If you go to the Ft Washita Monument, you will see a copy of them on display.
I see that Elizabeth Warren has also not claimed any benefit for being 1/32nd Cherokee. So the Wannabee comment is inaccurate and rather racist as well.
There is a very good reason that so many people claim to be part Cherokee: the Cherokee had a written language and kept written records in Cherokee. The other civilized tribes sent to Oklahoma (Choctaw, Creek, Seminole, Chickasaw) only recorded events (if at all) in English, and of course, most did not speak English and many fewer wrote it.