Correct me if I'm wrong...
... but isn't Cherokee the Indian tribe with the most caucasian influence? I am certianly not standing up for those who claim Indian heritage when they haven't experienced the inequality and racism of many Indians, but it's much likelier that a white person with Indian heritage would be part Cherokee than any of the mid or southwestern tribes.
(I agree wtih you though... I've known of students to claim Cherokee and get scholarships for college when they don't have an Indian bone in their body, while Apache and Navajo kids get rejected)
To keep it slightly on topic, I think for aesthetic reasons, folks wtih mixed heritage backgrounds should probably try to go with a more commonly American first name for their children. Just my opinion though. :)