IIRC, you only need something like 1/8th Indian blood to qualify for benefits or some such as an "American Indian".
While in school in NC, I met an "Indian" who had blond hair and blue eyes. It's funny to me because my dad's father's family is from a region in NC heavy with Cherokee (the rest of my family is from areas heavy with Tuscarora). My grandfather claims Indian blood and has many of the physical characteristics of Cherokee Indians (skin tone, hair, lanky limbs, etc). Even two generations or more separated from that "Indian" blood, I personally look more "Indian" than the guy I mentioned above (I at least have black hair and olive skin).
Anyway, regardless of my ancestors, I would not consider myself "Indian" any more than someone of Scandinavian descent. That my great (or great great) grandparents may have had some Indian blood is of no concern to me.
BTW, don't ever tell a Lumbee they're not real Indians, even if the person you're talking to has blue or green eyes.
I went to school with several, they're very serious about their "heritage".
Edit to add: Pictures of my paternal grandfather's family bear striking resemblance to old pictures of Melungeon families from that region of the US. My surname appears on a list of Melungeon surnames, but that doesn't mean much as it isn't exactly a rare name.
Edit again to fix my horrible grammar.
Chris