I suspect that the significance of the transponder reply (which the crew probably didn't see), was more relevant to a question of were the McMurdo controllers aware that the aircraft was descending towards Erebus so therefore why didn't the warn them? And if they indeed did, was it via VHF or HF? There has been a suggestion that some of the ATC tape had been erased at that time.
The crews decision/acceptance to descend was based on maintaining VMC, which they clearly had and went to great lengths to maintain.