Actually I believe it's an apple - orange comparison when we try to compare our attitudes towards FT and those of NZ population.
Well most countries are pretty specific on what they want, the folks here are vague. So in assessment for example when NZ says they want mechanics, they specify it's heavy vehicle mechanic and not mechanic in general. If they say they want an automotive electrician, they don't mean electrician in general.
Such specific (and also strategic) labour targeting allows only good and measured supply of manpower into the country. Even the targetted countries they invite are very specific. NZ is relatively bigger than Singapore with plenty of opportunities and resources. Will folks from Singapore make NZ a stepping stone for a future migration to other countries?
In Singapore, we welcome all kinds of folks with dubious credentials to make our country their stepping stone. They use us as a stepping stone because they can't be readily accepted in their ideal destination country (note: this is what exactly a couple of FTs tell me before the spat in media began).
For example, the USA does not welcome (not to mention approve) further migration from Vietnam, India and China. So in order to be eligible to settle in USA, a ROC will need to first become a Singaporean or Malaysian to be qualified in their green card application to the USA. And they are 100% fixated to their initial ideal destination and no amount of brainwashing will make them consider questions like "How about staying in Singapore?"
Singaporean do not need such stepping stones to go anywhere in the world, our passports are globally welcomed, so the arguement that Singaporeans will use NZ as a stepping stone is unfounded.
Talking about supply of labour, the FT in Singapore can choose to switch jobs and apply a job seeing your immediate career demise. In most other developed countries, initial migration detates the range of jobs you're legally allowed to take up unless you have become a citizenry there (not PR). So the problem with job leeching does not occur in their countries like our mess.
If job supply is a good fit to job demand, job leeching is not possible due to legal controls, the country is already one of the ideal destination country and that the place is bigger with lots more opportunity and resources, will NZ citizens see us like the way we see things in Singapore.
The answer is obvious.