AOC's and EBA's are two entirely separate animals.
At the risk of stating the obvious, the AOC is the regulatory operating certificate and doesn't care where the pilots come from.
The EBA on the otherhand cares where the people come from (I.e. Are they a party to the agreement) and doesn't care what rego is painted on the tail.
Jetstar has pilots in NZ flying VH tailed aeroplanes under a NZ agreement, same as Virgin, Qantas has cabin crew from various parts of the world flying on an Australian registered and operated aeroplane under agreements applicable to their domicile country.
WishIwasupthere has nailed it with regards the costs of shifting everyone to NZ to live just to get access to "cheaper" terms and conditions.