Earlier quoted context omitted.
Why do you find it cringe? In NZ I think it's even more true than Australia. It's a tiny, isolated country with a small population that isn't the hub of anything really. Aussie and NZ compared to the US are completely different worlds in my eyes. (I'm a Kiwi btw)
I think it's a myth that NZ "punches above it's weight" is all. Show me some empirical evidence if you disagree. I'm a Kiwi too - but living in Aus.
The obvious examples that come to mind would be sports. NZ excels in Sailing, Cricket and Rugby against much larger countries.
Though it could be that in general, Aus/NZ have the same skill distribution as other countries, but they just stand out more because there are lower expectations or highly skilled people are rarer overall due to lower populations.