He should. But she didn't go to Harvard as a student: George Washington University, University of Houston, Rutgers University, Newark. She's old enough that race wouldn't have been a factor at GWU and probably not at UH. Her claiming to be an Indian probably would have started later, when she was teaching at Texas, Pennsylvania, or Harvard.
I think I read she began the ruse from 1983 through 1996. It should not matter where she went but that she used lies to adhieve personal gain.