Mick, they were conducted under the charter company's AOC, not the RFDS. The RFDS would contract for the clinic run flight so as far as the company was concerned it was another charter. The RFDS set the minimum standards that the pilots had to meet and the company was subject to an RFDS audit prior to them agreeing to use the company.
The work I did for the RFDS was charter. However, the work I did on behalf of the Tennant Creek hospital was airwork on the company's AOC. The work I did out of Darwin was charter, again on the company's AOC. While I was in Tennant Creek I was occasionally tasked to do an evacuation which would otherwise have been done by the RFDS but for the fact they didn't have an aircraft available. However, this work was again through the Tennant Creek hospital and again was airwork under the company's AOC.
The whole issue of who is authorising the flight is perhaps a little clearer if you understand that all medical flights in the NT and possibly throughout Australia are at the request of the various State or Territory governments. The request goes through a government officer who authorises the contracted flight organisation to undertake the flight. In the south of the NT the flight organisation was the RFDS, in the north it was a division of Pearl Aviation (when I was there).
Apart from medical transfers and evacuations the RFDS runs an extensive medical service of clinics and GP practices. For example, the Tennant Creek GP is (or was then) an RFDS employee. It was established by the RFDS and staffed by them. It is primarily this service that the RFDS raises cash so heavily for. The aircraft side of it is a contract service paid for by the various governments.
I'm sorry that I didn't make that clearer.