The Census Bureau policy is irrelevant for purposes of this discussion. CU's policy is the relevant standard.
The application Churchill filled out stated clearly that the description Native American/Pacific Islander applied only to persons descended from the original peoples of North America.
Moreover, Churchill claimed Affirmative Action preference on his application. He was one of eleven Native Americans who applied for the job, one of two who were interviewed.
I rather doubt that the other Native American who was interviewed would feel quite so dismissive about Churchill's true ancestry as Mr. Lyons is.