This line of reasoning is entirely fallacious. The right is to be able to keep and bear arms, which like the freedom of religion doesn't mean you must have one. You can if you want.
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As for OP, it's the opinion of one very well off gun owner and doesn't actually address the vast majority of criticism of applying Australian like restrictions to the US. It does however show that guns aren't all illegal there, and people can still get them if they really want and have the resources to deal with it all. It's very useful for clearing up some misconceptions.
The 'is self-defense a valid reason' discussion isn't changed by this at all. Some people vastly overestimate the usefulness while underestimating the limitations of guns as tools for defense, while others continue to vastly underestimate the usefulness and overestimate the limitations.