Another problem with ACC cover is that it is very difficult to get them to pay out, this present government is responsible for that (for visitors and residents alike) and many claimants are told they're not covered because of some spurious pre-existing condition, even using excuses like wear and tear which has no bearing at all on the actual accident. For example, you could break your wrist playing basketball but not be covered for treatment if you've got "wear and tear" in one of your joints.
Personally, I think ACC is a basket case organisation in a government that lost its moral compass years ago. Incidents like this one don't help much
http://www.nbr.co.nz/article/nz-politics-daily-acc-scandal-goes-straight-top-ck-115386