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David_Gerard comments on Harry Potter and the Methods of Rationality discussion thread, part 16, chapter 85 - Less Wrong
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BTW - this was the accepted figure as of 1991, but molecular evidence suggests 62,000-75,000 years. Which makes Harry's point even more strongly: it took a long time for humans as we know them to invent what we think of as basic stuff.
At a cursory glace the date you cite seems to be for the time the population they are descended from split from African populations, not for when they arrived in Australia. Genetic evidence cannot show where your ancestors lived, only how they were related to other populations (which might imply things about where they lived provided you already know that for the other populations)
Genetic evidence can't show where your ancestors lived, but it can gesture furtively in one direction while mouthing "look over there". Even in hunter-gatherer populations, there's enough mobility that it shouldn't take anywhere near 22,000 years for African genes to make their way to Australia (or to wherever the proto-Australians were living at the time).
There's a big difference between a few people making their way over and genes achieving fixation.
I approve of your stealth xkcd reference.
Yes, you're right - this piece gives 50,000 years ago for the arrival.
But the point stands as to the minimum time humans were anatomically and cognitively modern.