He doesn`t claim to be 1/16th Cherokee. He only mentions that he is Cherokee. Every biography I read on this guy only mentions him as Cherokee. If he was 100% Cherokee then it would be impossible for him to have the name Churchill. Look, here`s some if you don`t believe me. Here`s some random bios of him I just found on the net.
Ward Churchill
From a Native Son: Conquest and Colonization in the Americas
Ward Churchill (Keetoowah Band Cherokee) is one of the most outspoken of Native American activists and scholars in North America and a leading analyst of indigenous issues. He is a Professor of Ethnic Studies and Coordinator of American Indian Studies at the University of Colorado. Churchill serves as Associate Director of the Center for Studies of Ethnicity and Race in America at the institution. He is also co-director of the Colorado chapter of the American Indian Movement and vice chair of the American Indian Anti-Defamation Council.
http://www.speakersandartists.org/People/WardChurchill.html
Ward Churchill is perhaps one of the most provocative thinkers around. A Creek and enrolled Keetoowah Band Cherokee, Churchill is a longtime Native rights activist. He has been heavily involved in the American Indian Movement and the Leonard Peltier Defense Committee.
http://www.satyamag.com/apr04/churchill.html
I had heard that specific figure either in news accounts or on some talk radio show (Glenn Beck? Rush?). I do wonder about the reports that the tribal council contradicts his claim, since they don't have any records on him--I really don't expect them to have records on every 1/umpteenth Cherokee out there (I'd be very surprised to find they had records on me). Yes, I am aware a 100% Cherokee would probably have a more Indian sounding name.
The bios you posted, the second one in particular, sound like they come from some leftist sites. Since they don't mention his exact fraction of Cherokee, it sounds like they're trying to emphasize his "Indian-ness," probably at his request. Sounds like white liberal guilt to me (on his part).