I guess it probably depends on the hiring procedures at each University. I can only speak to ours.
We give minimum and desired qualifications in our job ad. These have to be approved by HR and the Human Rights Compliance Officer at the university. We then screen all applications according to these criteria. If a candidate does not meet our minimum qualifications then it would be really tough to convince HR and the HRCO that we are doing our duty as an equal opportunity employer to bring them in for an interview. The desired qualifications allow for more interpretation on the part of the search committee, but even for this, there is a ridiculous amount of documentation and auditing that goes on to make sure that we are "fair".
My main point is that I think that the openness on the part of the department to non-math PhDs would have to be at the ad-writing stage. By all means, your friend should call and ask the department, if they are open to a PhD in a related field. Just don't be surprised if they have already tied their own hands.