Yeah, I've met a few RN/MBAs high up in hospital administration too (did the RN thing first, and then went back to business school later. And at least one JD/MBA. Point is, you often don't degree yourself to prepare for this job, you get work experience to prepare yourself for this job (be it medicine, nursing, law, administration), and then you can always pick up an MBA (once you have experience) to seal the deal. MBA's aren't prerequisites to jobs the way an MD or JD is -- they are basically skill enhancers -- things that are most useful to get once you actually have job skills. Which is why most of the better MBA programs require prior work experience, and why most MBA students have their tuition paid for by their employers.
I wouldn't go into a joint degree with notions of doing two jobs (administrate and be a clinician) -- you focus on one, and if you still want the other, you make the move later, and degree up as necessary.