Hospitals have different levels of priviledges, sometimes depending on specialty.
If you are a subspecialty surgeon who only occasionally comes in to cooperate on the care of a patient (e.g. a plastic surgeon to participate in oncologic ortho cases), you might only have 'consulting' priviledges without admitting rights. Some of these 'lower' levels of priviledges don't come with obligations such as serving on committees or call coverage (but also without the typical rights such as voting or dismissal process rights).
The paperwork hassle is pretty much the same, independent from the level of priviledges sought. They will allways check with your prior hospitals, verify your training and check on your claims history.