If the SA Investigators are allowed to investigate this accident then I am sure they will dig deep into the paper work...
Well, the South African 'TSB' (not sure what the exact term used is) will certainly be an accredited party to the investigation, because the aircraft was registered in South Africa. The American NTSB will also be accredited, because the aircraft was manufactured in the USA and also because one of the operators involved (AirServ) is an American operator.
The regulatory agencies (American FAA, SA CAA) are not directly involved in accident investigation, that is not part of the madate of a regulatory agency. They may become involved sooner or later (pre or post issue of the accident report) depending on the findings made by the TSB team that carries out the accident investigation.