Hi Becky,
I've never dealt with such a request, but I can speak to my views on the issue.
A student and faculty member insisting that the university archive a redacted thesis would be a huge red flag for me. It is possibly indicative of fraud or that the work does not meet the minimum requirements of the university for approval. Or it could be indicative that the research was unethical or conducted in such a way as to violate other laws, norms, or standards in the field.
More importantly, a thesis is a legal document of sorts. It is proof that the student completed that requirement for being granted a degree. The university could, theoretically, be compelled by a court to produce the document as part of a legal proceeding (perhaps a subject alleges that the study was unethical in nature, or a high profile employer sues for alleged inflation of credentials later in this person's career, or the university becomes party to an accusation of widespread fraud related to "paper classes" that never met and the accrediting organization demands this along with many other theses to investigate a pattern, etc.). If the university can only produce a heavily redacted document, that would be problematic to say the least. Imagine a university that can only produce a transcript with a list of courses taken, but the grades are completely unavailable, or vice versa. This is a slightly far fetched example, but not outside the realm of possibility. Universities have been compelled by courts to produce items in their closed archives in the past.
If the student and faculty member can articulate a reasonable case for the content of the thesis never being available to the general public (for example, protection of potentially vulnerable persons or populations, research that is considered classified by the federal government, etc.), then a permanent embargo is certainly warranted. But I, personally, would strongly insist that an unredacted copy be submitted for archiving and would have no qualms taking that insistence to the dean or even the provost.
In a very innocuous reading of the circumstances, it might simply be that the student and faculty member don't trust the libraries to actually respect an embargo. Perhaps this is a good opportunity for education on the standards of conduct in archives with respect to privacy, compliance with donation agreements, access controls, etc.
Good luck!
John O'ConnorScholarly Communications Librarian