According to a genealogist that did our family tree my great,great grandmother on my fathers side was Cherokee. If true that gives me at least as much Cherokee ancestry as many current tribal elders. And as pointed out if Warrens claims are accurate she has the same amount of Cherokee blood as the current chief. So if it's good enough to get to be chief seems to be enough to claim.
Claiming ancestry for Native Americans is quite different than claiming black (say) ancestry. There are strict rules for proof.
Here is how you register as a member of the Cherokee Tribe.
Here is another link. You are right, if Warren can fill out one of these forms, and have it accepted and she can become an enrolled member of the Tribe, than she (and you) should by all means claim ancestry.
But if she didn't do that, than no, she did not do as much as the current chief.