I think part of the rationale was that:
-they need someone who is an excellent association manager, first and foremost, and
-she won't have any prejudices one way or another about chapters.
Many of the fraternities have female exec directors so they obviously weren't members.
Her job is to run HQ smoothly - not to make or enforce policy for the sorority. That is the duty of the national council. As long as she has a working knowledge of Greek life, it shouldn't be a problem.