Once you meet some Australians it will all become clear: they consider themselves to be honorary American citizens, and their country is actually the United States of Australia. Seriously, everything about Aussie society and culture is consciously imitating that of the U.S.A. - which is pretty sad, I'm sure you'll agree.
Either you are just trying to be funny, or you have obtained your "facts" from some strange source.
I'm an Australian, and I have NEVER thought of myself in the way you mention; honorary or otherwise.
The official title for our nation is the Commonwealth of Australia.
Mainstream sports include Cricket, Australian Rules Football, Rugby League, and Rugby Union.
Australian traffic has always driven on the Left.
Our navy is named the Royal Australian Navy, and our air force is named the Royal Australian Air Force.
We have a Governor General and individual state Governors as representatives of of the Australian monarch (currently Queen Elizabeth II).
"Canada, Australia and New Zealand are clearly not controlled by the United Kingdom. The monarch of these countries (Elizabeth II) is in law Queen of Canada, Queen of Australia, Queen of New Zealand and only acts on the advice of the ministers in each country and is in no way influenced by the British government."
Oh yes! That state of affairs is so clearly 'imitating that of the U.S.A'.