My father is full blooded Chiricahua Apache and my mother is Czechoslovakian. So I am half of each. I don't get any tribal rights as my fathers ancestors fought to stay off a reservation, and therefor I am not registered with any tribe. No tribe will accept you as a member of there tribe unless you can prove they are a registered member or had someone registered in there bloodline. As for all the people that clamed 1/16 I don't think you qualify anyway's. Check out your local tribal rules and laws.
I consider myself an American, I tell everyone I am American. But due to the PC B.S. that everyone needed a special name such as African American, Asian American etc, I am considered Native American as that is more my skin color. I cannot clam my mothers side, as I am not light skinned enough to clam white.
I do have a problem with all the other people saying they are African American, Japanese American etc. Pick one country and stick with it, you are either African or you are American, you are Japanese or you are American.
As for Native American, I don't really see a problem with it. When someone ask what is your ancestry, you can say Irish, German, African etc. What is someone that is Native American suppose to say? So Native American seems to fit.