Just be careful about biological material (NZ has very strict airport biosecurity) and you'll be fine. I'm a New Zealander and this is the first time I've heard of something like this happening at the border.
I remember when we visited the Philippines, a friend gave us about 20 jars of a local delicacy to take back home to New Zealand. Which was very kind, except New Zealand's biosecurity laws meant that we had to throw most of them away at the border. (We could keep the few that were sealed properly.)