In the US, many Medical schools are schools only in the technical definition of schools. In reality they are more like research and medical centers that also do a bit of teaching on the side. Staff to students ratio could easily be in excess of 10:1

A little over a decade ago, I remember Dean of a top medical school I attended showing the budget of the medical school. Tuition was like 5% or of the entire med school revenue and budget. I remember raising my hand and asking the Dean if tuition was so little, why not just make it free. He gave me a death stare and just danced around the question.

I mean, if you tack on a hospital to a university, the correct denominator to compare against is "patients served," not "students educated," at least for the portion of the headcount you're sticking in the numerator.