My ex's family went and worked in Australia for a year or two. They boarded the plane, came back to New Zealand, and got a letter from the IRD demanding payment of taxes for the time they worked in Australia. Her father shot back that "They did not use any services from" NZ at all. The IRD responded that the services were available, and if they didn't pay their tax bill they were ready to initiate prosecution.
In general, that is not the law, nor is that common IRD practice, as the many, many, many kiwis who spend time in Australia could tell you.
At a guess, your ex's family managed to stay resident in NZ (or the IRD may have incorrectly believed them to be so), or they spent too much time in NZ, or didn't spend enough time in the US, or the IRD just screwed up the paperwork, etc.
Did they fall foul of having "A permanent place of abode" in New Zealand? It seems that the IRD will consider you a resident in NZ as long as you maintain a house there, regardless of how long you stay away.
My ex's family went and worked in Australia for a year or two. They boarded the plane, came back to New Zealand, and got a letter from the IRD demanding payment of taxes for the time they worked in Australia. Her father shot back that "They did not use any services from" NZ at all. The IRD responded that the services were available, and if they didn't pay their tax bill they were ready to initiate prosecution.