No, I don't think you are wrong - that's what I think, too.
Here's a link to a list of what healthcare services are free, and which you have to pay for: http://www.newzealandnow.govt.nz/healthcare~279.html
Under the public system, essential heath care is provided free to all residents. This means that while some routine services, such as visits to doctors and dentists have to be paid for, more costly services, such as hospital treatment are available free to all residents.
Publicly funded health services include:
- Free public hospital treatment
- Free 24-hour accident and emergency treatment at public hospital clinics
- Subsidies on medicines and prescription items
- Subsidised fees for visits to General Practitioners (GPs)
- Subsidised fees for specialist care
- Free or subsidised health care for those suffering acute or chronic medical conditions
- Free x-rays and most laboratory tests, except at privately operated clinics
- No charge for health care during pregnancy and childbirth unless you prefer to use the private sector
- Free breast screening for women between 45 and 69
- Subsidies for children under six for visits to the GP and for prescriptions
- Government-funded accident compensation (ACC), which applies to everyone, including visitors to the country.