Welcome to allnurses!
I've been faculty in a couple of different nursing programs
and directly involved in arranging clinicals. The short answer is that hospitals and other clinical settings reserve the right to refuse any
student, for any
reason. Schools are correct in telling you that they can't guarantee that you'll be able to complete clinicals. At the last BSN program in which I taught, the school only did background checks because the clinical facilities insisted on them, not because the school cared (on the other hand, I did have concerns about the school being willing to accept and take tuition money x4 yrs from students who they reasonably expected to have problems getting licensed, because of their legal history, without saying anything to the students. When I asked the program director about the ethics of that, I was told that students' legal background and possible difficulty in getting licensed was between them and the BON, and not the school's concern).
Sorry I can't give you any more positive info than that ... Best wishes! I hope you'll find a way to work things out.