May I raise one point which seems to be missed by many.
The Commander of the USN Support Force Antarctica had advised the airline, "Air traffic control/flight following shall take the form of location advisory of DEEP FREEZE aircraft and position report only."
The airline in its briefing sheets advised, "Descent to be co-ordinated with local radar control as they may have other traffic in the area."
Hence any mention of the aircraft requiring, or having, authorisation or clearance to descend, or to do anything else, is mis-placed, as all the crew had to do was advise McMurdo of their intent and effect their own seperation from any other traffic. Nor was the descent required to be radar monitored as has been suggested.