Dealing with INZ is something that an employer offering a skilled job to a foreign worker has to factor into the situation. It's not the employee's fault if a visa hasn't been issued by a desired start-date, any more than it is the employer's, and the time it takes beyond the control of both parties, because it depends on how many applications INZ have got queuing. The employer is supposed to have good workplace practice
https://www.immigration.govt.nz/opsmanual/#66792.htm, including abiding by NZ employment law, which would make it just as illegal on their part if you started working without a visa as it would be for you to do it. I'm just thinking aloud here, wondering if this would give you any points for answering the employer's argument/threat - how does it sit with the small print of the legal offer of employment, for instance, if they now try to push you for a start-date that wasn't in the original paperwork that you signed, and that INZ have to hand?