Our head of school was brought in from the outside to “help navigate the new challenges in academia” (I.e. to make cuts). They hold the title “professor” (which outranks doctor by quite a bit).

During one of those awkward “get to know you” talks I just asked what her research speciality was (common icebreaker among academics); turns out she wasn’t a researcher, had never done a PhD, and had gotten the job on managerial experience.

In cases like this, the joke is that “oh, so the chair is the professor” (it’s common to become a professor when head of school, you lose the title when your rotation is over); in cases like the OP it should transfer to “oh, so your wallet is the doctor”.