You are unable to use a Private Box address as a proof of address. We are a postal address only, and you cannot claim that we are a residential address for any reason.
I want to set up a New Zealand bank account - but I don't have a New Zealand address
You cannot use a Private Box address for setting up a bank account. You can use our address as a postal address only.
Many banks do have options for international customers to set up a New Zealand bank account, using your overseas residential address as part of the verification.
Here are some links to different banks in NZ (in no particular order) -