Actually I believe it is, cabinent level that is. CIA isn't part of any other agency and the head of the CIA is more than just the head of the agency, he's also the head of the "intelligence community", which includes other agencies, and portions of the military as well.
However the Constitutional provision speaks to "civil officers" not which goes way beyond cabinet level, to every civil servant, career or "political" appointee. In fact the notion of the "cabinet", like the notion of political parties, is outside the provisions of the Constitution.