But as you note, that’s the military route, for aircraft landing at McMurdo Station. Obviously, none of the AirNZ flights intended landing at McMurdo Station – which is why none of the flights made any left turn at Byrd. They usually went to the right of track to get a closer view of the coast of Victoria Land, and then turned left towards McMurdo Station, passing the general Byrd location on the way.
But they would need to make the left turn in order to carry out the NDB approach should the weather dictate. What each crew actually did was make a judgement that they were in VMC and descended accordingly, just as the fateful flight.