PIC - ICUS
Folks, it does not seem to me to be ambiguous. Surely, if a pilot is under supervision he or she is being supervised by one in higher authority. It really should not take a Rhodes scholar to determine that when a pilot is acting as pilot "In Command Under Supervision" he is training or being assessed to be promoted to act as PIC subject to meeting a predetermined competency level.
The "Supervising" pilot is the actual "Pilot in Command" and is the one with responsibility for the safe conduct of the flight. Seems fair enough to me and I fail to see why the supervisory pilot should not log his hours as PIC. Obviously, if Kopity has it correct, the NZ authorities have a different view and that is their business. How they justify their view is of interest all the same.