NZ is known for making things as difficult as possible for partner flights. I am not sure about the point of these endless restrictions for an airline that they are supposed to call partner.
I recently tried to book a flight to Lima and found that not only NZ have removed Star partner connections they have limited to AR in Economy only even if you book a Business fare. You would think that AR being their high profile South American partner they would make it easier for connections. But sadly no. Even worse, no Airpoints accrual apart from Rio and Sao Paulo. In the end I booked VA to LAX instead. Would really like to try their new EZE service but wasn't meant to be.