In my view it depends entirely what you mean by 'Cherokee'. With extremely high probability (like 99.99%+) she has a significant amount of Native ancestry. That ancestry is probably from the continental US. Since she's from Oklahoma, that's probably Cherokee.
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There are some confounds (like there's a plausible but very weak argument it could be Siberian ancestry via Scandinavia) and it's very unlikely that it can be pinned down to a specific tribe unless they find actual matching Cherokee relatives.
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There's also a legal/moral/spiritual/supernatural argument that being Cherokee is a mystic status conferred by the tribe itself and if some oil contract manager in Oklahoma disavows her, that's the end of it. Some people take this argument seriously.
End of conversation
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. Banned in Sweden. SubGenius, Zhuangist, white-hat troll. Defrocked mathematician. Brain problems.