Now, this is kind of contradictory to what INZ told me 5 months ago about entering NZ... I was in my country of origin and wanted to renew my passport then (to avoid hiccups). I didnt have enough time to renew the passport AND transfer visa label to new passport (through London office). I asked INZ if I'd be allowed to enter with a new passport (with valid visa "in the system", but visa label not transferred yet). They said no... What do you think? (I understand this is a different issue, i.e. entering the country). Many thanks!
No, it's not a contradiction, because that is a different situation. Nobody is allowed to travel on a new passport when their visa is in an old one, and only linked to that old passport in the computer.
In the present case, you aren't trying to use your passport to travel.
Many people have reported the same thing, that what they are told by INZ can be different on different occasions. INZ telephone answerers are a kind of human FAQ working from a database. They're not qualified case-workers. As you know yourself, you can get different answers from a database depending on which areas you access, which in turn depends on what key words you enter.