I can see why the first sort of situation would reflect badly on the doctor. But what's wrong with the second sort? It's not as if McCoy would have work to do elsewhere.
On the other hand, the pilot episode introduced us to the Starfleet desire to observe the psychological well-being of its deep space crews. McCoy is an expert in space psychology ("Court Martial"); perhaps, just like Spock combined the jobs of XO and SO under one brilliant head, McCoy provided Starfleet with the services of both Dr. Dehner and Dr. Piper on one salary?