Are birth, death and marriage records not public?
I don’t know about New Zealand, but nowadays in Australia recent births deaths and marriages records are only available to their subjects and close relatives. Two reasons (a) privacy (b) helps prevent identity theft, since birth certificates (and sometimes also marriage certificates) are often accepted as identity documents
I organised one for my grandparents a couple of years back. They also received a card from the Prime Minister [of New Zealand], the Leader of the Opposition, their local MP, and a couple of other random politicians and dignitaries.
It's not something that I thought about at the time, but I'm quite happy that it's something you need to apply for. It would be a bit disconcerting if the Queen had access to the birth, death, and marriage records of everybody in New Zealand.