Actually, what they're short of *is* managers - and secretaries and other admin staff. Admin doesn't go away just because there isn't a dedicated person, it just means the doctors and nurses are having to waste their time filling them in and handling them instead of treating patients.
A boatload of admin people can get hired pretty quickly, a lot faster than new doctors can - get them in now, and you've got doctors doing doctoring and admins doing admining, and you're getting some actual efficiency due to people working on what they're specialised in.