It seems unlikely that the witch doctor was working under the NHS in Africa. I think the issue could have been that Captain Smithers didn't have insurance to cover whatever treatment he required, the witch doctor may not have been willing to treat him without some payment upfront.
The story is incomplete, I want to hear about the day he decided to tell the Witch Doctor to f*ck off. Was the witch doctor understanding? Did they have lunch? What was the weather like?