It’s a very simple affair that has been mucked up by her campaign.
She’s Oklahoman, probably half of the people there have Native American ancestry. She’s also a 70 year old woman, so it’s quite feasible that in the 1940s when her parents met, one of them being from a family with ‘known’ Native American ancestry, even if it’s a few generations removed, would be frowned upon by the other’s family and close relatives. At this point, we have no reason to believe that she Rachel Dolezal’d the whole thing up, knowing the story and details she gave. Many among us have some sort of fables passed down in the family about having this or that figure generations past, most never bothered to do an ancestry test to verify.
The problem stemmed from her listing her ethnicity as Native American in a few forms. Now, I can’t claim to be privy to her thoughts, but there are two possibilities here, a) she genuinely believe in the family story and proud of that, and use Caucasian/Native American interchangeably throughout her life, that we need more info to ascertain or b) she used them for diversity hire, which in the grand scheme of things either personally or professionally not a big deal, even though not savoury, especially when you take into account her circumstances, divorced with a kid to raise and being a single mom in the 60/70s.
Ignoring Trump altogether, or at worst a candid conversation with admission of the possible way the claim might have benefited her professionally would have been better than the ancestry test, but hey-ho.