Snopes have a decent write up too.
https://www.snopes.com/crime/statistics/ausguns.asp
That said there may be a level of truth to the claims that people have at least been put on trial for killing home invaders, but in Australia our laws are different and you just can't expect to kill someone and call on self defense to get you off. ALthough it is complicated.
Another good write up about home invasions in Australia and how the law differs from the US.
https://theconversation.com/how-far-can-you-go-to-lawfully-protect-yourself-in-a-home-invasion-56900
But yeah, it is mostly nonsense claims. Pretty much all of the above is a non issue in Australia.