I don't think that anyone claimed Warren had done the paperwork to establish herself as a member of the Cherokee Nation, so this is all a massive strawman.
So let's put aside the desperate wingnut swift boating aside for a minute and look at what probably REALLY happened? I'm sure that, like many native Oklahomans, Warren was told growing up that she had Cherokee blood in her family, and she had no reason to doubt what she was told (which, as it turns out, was true). So like a lot of young people filling out applications, she mentioned stuff that she thought would make her sound interesting. "Hey, I'm part Cherokee -- pretty cool, right?" And that is what all this bull**** is about. In fact, all of the institutions that have responded have said that they either didn't know of the claim or it was immaterial in their decision to bring her on board. And it seems that at least one of the institutions did essentially the same thing, i.e. they published in some directory that one of their profs was part Cherokee -- pretty cool, right?
And what about your claim of fraud? In all likelihood that, too, is bull****, for several reasons. First, fraud requires intent -- knowledge of the falsity of the statement and the belief that it will have a material effect. In this case it appears that Warren thought she was telling the truth. Second, fraud requires reliance on the false statement by the recipient, and there is no evidence of that. Warren made no representation of Cherokee ancestry to most of the schools she applied to, and the others have said that they absolutely didn't rely on the claim in making their decision to take her on. And finally, fraud requires actual damages and there apppears to be no evidence of damages. Rather, the schools that Warren attended and for which she worked have benefitted from their association with her.