I did a stint working for the US BIA some years ago, so I can offer some info on this.

There are two factual predicates to being "Indian" as that word is used in the US Constitution; 1) you must be able to document that you are at least one quarter "Indian" and by doing so can receive a "Certificate of Degree of Indian Blood" (CDIB) which entitles you to rights and benefits reserved to federal Indians; and, 2) you must be a member of a "federally recognized Indian tribe," a list of which is published by the US BIA. Normally, only those "tribes" which at some time had a formal treaty relationship with the US are considered "federally recognized," but politics has crept in from time to time and various "groups" have managed to convince the USDOI or the Congress that they are deserving of recognition.

Frankly, like everything associated with the USBIA, the whole CDIB and federal recognition process has been fraught with mischief and corruption since time immemorial and it is fair to say that in the East and West Coast states especially, and I'd include the Creek, Cherokee and associated tribes among that group, "Indian" is as much in the eye of the beholder as any matter of blood or treaty relationship.

We who do WBTS research are all acutely aware of how difficult it is to identify our relatively recent and relatively well documented ancestors. Think what it would be like to go two centuries further back in societies that had no written record and very different matrimonial and "parentage" standards.