Does it matter? When an Aussie says "this was built by an Australian", they're really saying "Australia, the underdog nation, produced something that would normally be associated with 'them out there' and we should be 'proud' of it" .. in order for that congratulation to work, Australia has to be an underdog nation, and by association, Australians too.
It reeks of jingoism every time we see an article in an Australian media organization about Australians 'making it on the world stage', and just induces cringe, imho. (Disclaimer: Australian living in Europe) I've never seen any positive response to this kind of pitch: its always "oh, those Australians think they're so poor, and congratulate themselves at the drop of a hat" .. I think its one of those activities that doesn't have the desired effect, at all ..
I'm American but have Aussie PR and very familiar w/ the culture ... I agree, the cultural cringe in Australia is still really bad. I spend a lot of time online and in-person convincing Australians that whatever they happen to be whinging about Australia is actually far better than most anywhere else in the world.
Americans are the complete opposite, we refuse to accept that we aren't the greatest country in the world, an exceptional people guided by God himself to greatness (imagine that).
Two extremes. Both have their downsides and upsides, though.