Actually, their study didn’t get into why the students’ self-assessments of competence were skewed. It could be from many reasons - social stigma of pride for the competents, embarrassment for the incompetents, incompetents’ inability to think logically and impersonally, or, your favorite, PC ideas about equality of ideas, to name a few.
They did say that incompetent people seemed to be much less able to accurately judge their own and others’ competence.
Their questions were constructed to avoid the subject in a very specify manner. Like I said, I believe it's a false study. YMMV