Yeah, you have to wait for months in the US, too. I have no idea how this talking point got started but whoever came up with it clearly hasn't dealt with healthcare in the US. Months-long waits for non-emergency appointments have been the norm for decades.
That doesn't mean to say that it's as bad as in the US, but it does exist.
I'd also go out on a limb and say that there are more poor people in the USA than in Australia per capita, which might factor into how many people can't afford healthcare.