AirNZ didn't tell him to fly down that hole. He made that decision all by himself, on a whim.
He started the day by not noticing that the 166E he punched in (or read out) was not the 164E he had plotted the night before. He didn't check the waypoint on the way down, probably assuming blue skies. When he didn't get those conditions and was going to go somewhere else, he was offered the radar letdown, and accepted. So that was the plan: Stay above MSA until the ground radar has confirmed the aircraft's position, then descend. With that plan, the position of the waypoint was not critical. If he had stuck to the plan, the aircraft would have flown over the summit of Erebus, whereupon the VMC radio would have burst into life. But then, about 40 miles out, he spots the sea ice through a hole in the cloud, and very shortly thereafter, he's orbiting down through it. So he dumped a good plan, with hardly any discussion with the rest of the crew, and replaced it with a very bad one, namely, his VMC/AINS plan. VMC below the cloud could not be assured, nor could the position of the waypoint, which was now critical. At that point, things on the flightdeck would have become very busy, hence the sounds of paper-shuffling and the references to high ground. This was probably why they did not notice that Beaufort Island was not where it was supposed to be, despite going past it three times.