Most of us Yanks -- at least those of us of a certain age -- know this, but, for anybody who doesn't:
The Citadel, where (as you correctly said) much of this episode was filmed, became the focus of a big controversy some years ago, when its commandants fought extremely hard to prevent it from becoming co-ed -- a striking parallel to the "Columbo" plot (but without the urinal-based clue). It was really a case of "Life Imitates Art".