Sounds like the call centre was trying to be helpful and is trying to give you an honest estimate of the time. I've called them a couple times and found them to be very helpful and informative but they do have their hands tied a bit because they can't see exactly what is happening with the visa process.
INZ really does need to update the estimated processing periods on this page, they are completely different from what they will tell you on the phone:
https://www.immigration.govt.nz/abou...sa-application
Anyone who wants a processing estimate should just disregard this page and call INZ and try to get advice directly from them. I made the mistake of relying on that page and expected a 4 month processing period. After about 3 months without hearing anything from INZ I called and they said partnership-based residency visas were estimated to take 4-9 months for processing...quite different from "4 months!" It ended up taking about 5 months, and I applied from overseas so it might have taken even longer if I'd applied from within NZ since they supposedly give overseas applications a bit of priority. 5 months was fine but it was worrying hearing nothing and wondering if it could really take 9 months since my overseas residence visa was expiring about 6 months after my initial application lodgement date.