You left off the part that answers your question:

> (something nearly all university presidents have)

So yea, it looks like it would normally be a disqualifier. I'd imagine it's for the same reason that not being a part of a union means you can't be leader of the union.

Or why Boeing should probably have had a signification number of engineers at the top levels over the last decades.

EDIT: There's a peculiar meme that I first noticed in the early 2010s that it's actually good to not know anything about what you're doing because you can "innovate" and "disrupt" better. I remember first hearing it explicitly stated by the founder of B.S. startup uBeam. Wonder how that's turning out...