You're right. And my "Countries Distance Matrix" concurs. Seems like next up is surprisingly- Uruguay, at 6465 km, narrowly beating out Turkey. Though that should probably be confirmed by whatever source Quizmaster is using.
I finally got around to writing a computer program to calculate distances. I dug a little deeper and it seems that Australia is 6397 km from Marion Island, an uninhabited island controlled by South Africa. I think I'll remove that answer and add a caveat.
All but Uruguay. I tried Argentina and Chile -- figured if those were no then Uruguay wouldn't work. I should know better by now than to not at least try what I think is unlikely.
As statet in the top.
The Falkland Islanders are British citizens.
Also, the Taiwan comparison is inadequate, since Taiwan is a sovereign nation, unlike the islands.
And I knew I forgot one country in the Saudi Arabia area, forgot about Kuwait.
But Kuwait was the last one I remembered.