I found the same issue with my Family in Indian Census showing the family listed "white" when it was my belief they were Native American.

I was very confused as to why my Family would list themselves as "white" when I was led to believe for the last 10 years they were Choctaw Indian living in Indian Territory. In fact, my Great-grandparents were married in Coal County, OK Indian Territory in 1892 and gave birth to their children there, My grandmother included, so it was naturally assumed they were "Native Americans".

What I found was that my family moved to Coal County, Indian Territory in the late 1800's when the territory was opened up to whites to work the land and teach the children. My Great grandfather worked on the railroad that was being constructed throught the territory and subsequently married and raised his family. If his wife was Native Indian, I have not proof as she too was listed as "white".

To prove your Native American lineage, you should search the Dawes Roll or go to National Archives and search. It's a tough search, takes a lot of time and effort, but you might find your family there, or not.
http://www.archives.gov/research/native-americans/

Good luck