I never heard this statement before, however it is opposite. It's like Canadian English mix of British & American English.
Do you mean.......??
Why do North Americans think the Australian English sounds like British accents?
Then here is the actual truth.
People from Britain and Ireland first came to live in Australia in 1788. They brought many different kinds of English dialects with them.
Australian English was also influenced by American English because during the Second World War there were many American soldiers staying in Australia.
Also American television shows and music have been popular in Australia since the 1950s.
I hope this is the right answer to your question.