First up, have a read of this
That seems to me to border (sorry) on ridiculous. Applying the logic (and I use that word lightly) then
a) Anyone bringing a laptop to NZ and working on it for a foreign company whilst on holiday here should be denied a visa unless they have a work permit
b) Someone who arrives for a 2 week holiday and has, say, a PA with them should expect the PA to be denied a visa - and themselves, if they plan on working at all
The rules are clearly not intended to prevent someone minding the children (unpaid or frankly even paid) of a family that they are travelling with on a short one week trip to NZ from Australia. They are supposed to stop people coming here and actually getting NZ employment without a work visa - not carrying on a job that is not a NZ job, does not have any base in NZ and where they have no intention of living beyond a short holiday.