Plus, Cypress, they have subsidised care but not "Universal Coverage"...
Lookup "New Zealand health insurance" and read why there is a need to get such a thing in "Universal Healthcare" land...
Here's one of them for you:
http://www.everybody.co.nz/page-0a4164ca-3942-4d25-a6af-fa77aac8de68.aspx
Notice how long-term care isn't automatically covered? Doesn't sound hugely "Universal" to me... So, it is a progressive system of subsidies, but not "universal" at all. Much like in the US. If you need it you are more likely to get larger subsidies.
In order to move there you must pretty much show you will have no need for such subsidies. Health Insurance is sold for those that do not need the subsidy.