I'd say it has more to do with the fact that all major parties in Australian politics up until the 1970s supported the White Australia Policy. In varying shades since then no Australian Party has fully supported broad immigration policies, and have instead decided to marginalise groups for electoral gain by creating a sense of Australia being under siege from immigrants, which is a claim that has no basis in reality. Thus those in power are creating a societal 'other' that they can easily blame for problems. Further, segments of the media push this anti-immigration line, despite the fact that the statistics tell a different tale.
So yeah, I blame those with power and those with the power to stop those in power. A mythologised history, as you said, does undoubtedly play into the public consciousness, but that has been shaped very carefully by governments over various periods. Every government has had its own vision of our shared history and will glorify certain time-periods and aspects.
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