I'm not saying it is easy (it often isn't) but government provided accident insurance is provided to all (visitors included) within New Zealand. It provides medical cover and compensation for accidents for pretty much all situations. Wen you have a straight forward accident all is easy and it just works. The trouble arrives when you try to define accident or your injury was difficult to pin point. Botched operation? You might be covered. Infected mosquito bite? Not an accident, not covered. Infected insect bite? Accident, you're covered! Swallowed a chunk of glass? Accident IF it caused injury. No swallowed foreign body is classed as an injury unless it caused damage. Administering and defining this crap must often cost more than just paying out would. If you're filling out the paperwork, be very careful to write as little as possible and use the broadest terms possible.