Captain Roger Dalziell's flight, which because of unfavourable weather took the alternative sightseeing route over the South Magnetic Pole.
So it was possible, because of weather, to use judgement to alter the plan.
Re the radar,
The captain of a USAF C141 Starlifter following 49 minutes behind the Air New Zealand flight said no terrain was visible and he made a long gradual descent over the water, navigating entirely by the inertial navigation system and maintaining 16,000ft until being picked up by McMurdo radar about 38 miles out.He immediately entered cloud on starting his final descent, passing between layers with good visibility but no sight of the ground until the aircraft broke out of cloud at about 5,000ft and landed normally at McMurdo