Prospector, the problem with 'thoughts', 'assumptions', and 'mistakes' is that those who have them don't generally know it. The differencing between thinking something and knowing something is that in the later case you can not be wrong. A person who thinks something based on assumptions most likely is under impression that he knows it until something shakes his mindset. This makes it exceptionally hard to guard against.
One thing you can do to guard against it is to have a set of clearly defined SOPs and a company culture that makes it clear that these are to be followed. ANZ appears to have had the SOPs in place, but no one was following them. This is not to say that the pilots were blameless but that they had been setup as the last line of defence in the error chain. As the last line, they screwed up, but they should never have been put into that position in the first place.
Deadhead, you said:
The Captain’s decision to descend below the route MSA of FL160 was probably flawed, since under an IFR flight plan the only two ways you can do that is by descent under radar (or DME step or similar) OR by conducting a visual approach. (Of course you could cancel IFR as well). None of these things actually occurred, since a descent “VMC” is clearly not the same thing as cancelling IFR and proceeding VFR, and neither is it the same as conducting a visual approach. A descent maintaining own terrain visually still, as I understand it, requires a radar service. You cannot do that in a non-radar environment – you have to formally cancel IFR OR fly a visual approach.
Are you sure that you can not cruise below LSALT on an IFR flightplan in NZ? In Australia you can (in day VMC) but I accept that there are different rules for different countries.