Well as you say there is the astronomical phenomenon, such as seeing the 'southern cross' not seeing the north star etc.
This isn't limited to Australia and includes the South Pacific, including NZ, presumably includes South Africa, South America etc. Certainly the reversal of seasons is a big hint that you aren't in North America.
Then so far as whether Australia or New Zealand is part of North America which has been sealed off by the authorities? Well assuming that you can simply accept that people are so helpless and governments to powerful (the US is actually a great example of executive government failure), you can't get over the difference in Flora and Fauna. Both Australia and New Zealand have unique native flora and fauna which is not found anywhere else. Also we don't have animals that are common in the US, such as bears, coyotes, etc. Even assuming you discount Australian Marsupials and Monotremes (Echidnas and Platypus) there is the difference between Australian flora. Eucalypts, Australian Pines have leaves not needles, etc.
Your co-worker seems like an idiot who has taken cartesian doubt too far.