His hands may be tied. Certainly Duke gets federal funds even though it's a private University. Would the University be open to law suits by keeping out protests? I would think, however, that the group could be restricted to a particular section of the campus so as to not interrupt the students' lives, especially during finals week.
I suspect even if his hands weren't tied, he wouldn't do much with them.
All I know is, when I asked my student about the media being outside the dorm, all I was told is that the students were told by the RA that they (the media) had a right to be there. I do not know the particulars.
As head of a major university, Broadhead would have been more professional first allow students to complete their exams before permitting such an organization access to the campus...if at all.