Perth at peaks is about 2 average points higher than Auckland [0]. UV index does happen at peaks too.
I've met plenty people here who "never wore a hat their life" and look like a prune. Personally I'm more comfortable at home than trying to find a shade everywhere you go.
Don't know about Australia but when I was on Kerguelen island which is at the same latitude as my homeplace on the coast of France, there was a very noticeable difference in UV content, you could absolutely burn in just an hour without protection (and it happened often).
I live in Western Australia, which is much sunnier than anywhere in NZ, and this sounds hyperbolic to me.