I take it then that AINS alone isn't good enough? (Or is it, provided you've checked the actual inputs with a map?)
Normally you cross check with an independant system in order to ensure that you are in fact where your screens are telling you. Probably the most common method is to use a VOR and check which radial you are on and then check the distance from a DME, but you can use any method you like to satisfy yourself that you are where you think you are. If you don't have a DME you generally either have to get visual prior to going below MSA or overfly the station or be identified by radar.
I'm not familiar with Air NZ SOP's from that time (or now for that matter) , I'm not suggesting it was an SOP to do this check.It's just a way of ensuring that you are where you think you are prior to descending towards the earth.