This point is very country specific. In Switzerland, for example, the general rule is that insurance will pay a maximum of twice the theoretical amount of treatment in Switzerland. However, New Zealand (and many other countries) have a much more expensive health care system, which means that without additional travel insurance you could get into debt in the worst case. Therefore, it is advisable to take out additional travel insurance for the duration of the trip. The exact insurance criteria should be read carefully to avoid surprises. The 1-year insurance of Allianz cost me 235 CHF (about 250 Euro) with 1'000'000 CHF medical expenses coverage. It should be noted that this insurance and many other insurances can only be taken out if one does not deregister at the place of residence/community. Otherwise, a significantly more expensive international travel insurance can be booked. The exact conditions, however, should be evaluated by each exactly itself, as it is very country-specific.