You shouldn't need numbers to evaluate a proposition with a premise that is self-evident.
I mean, correct diagnosis is one of the first and most fundamental things a hospital does when admitting patients. Failure at this stage cascades through every step that follows, possibly with fatal consequence.
If you're "managing" a place that handles this work without a working understanding of the process involved, there's a very good chance that failures can be traced - in large part - back to your desk.
I have grown to not believe in anything as self evident, anymore.
Directly to this premise. Correct diagnosis is a difficult and often error prone things that a hospital can do. To think you can train someone to be a manager and be good at diagnosis is putting a lot of trust on someone.
Should they be able to help? Certainly. But, at some level, I would expect the manager to be better at knowing which doctor to get you in touch with moreso than how to do the diagnosis themselves.
I think there's an important difference between knowing how to do something well (i.e., on a professional basis), and having a basic working understanding of what the process involves; its inputs and outputs, the most significant enablers of success, the most pernicious sources of failure.
When it comes to the people I manage, I don't need to be able to do their job, but I do need to be able to speak their language and understand their concerns well enough to see the task from their perspective.
I should add that this has always been self-evident to me. And it's always worked very well. But I should also note that it's not the norm, and when people I work with discover how much I know about what they actually do, they're almost always pleasantly surprised. "Oh", they say "you really get it."
Nearly everything about management gets easier if you're starting from there.