Can my company do this?

I've been a tutor for an online tutoring company for the past two years. Recently, I've applied for a teaching position at a university and have started the interview/hiring process. As part of their process, the university that I've applied to has asked that I provide a list of current managers/supervisors who will fill out a job skills survey that basically ranks my skills in various areas. Well, my current employer has told me that my direct supervisor isn't permitted to complete this survey because she's not a "manager." Nor is she able to provide a recommendation for me. At the same time, upper management who is allowed to do so will not because they employ "1000+ tutors" and cannot fill out individualized surveys. So essentially they're saying that they won't give me a recommendation, even though I've been an outstanding worker. Is it legal for them to dictate what my supervisor does? Because that doesn't seem right. The top of the survey even says, "Your responses are personal and do not reflect the views of any company/organization to which you belong now or to which you have belonged in the past." How can she not be allowed to fill this out? Isn't this some sort of rights infringement? It seems like this company is trying to dictate how/when their employees can seek employment elsewhere, and that can't be okay. Anyone know anything about this?