Melbourne

Definitely a few slightly more forceful reasons why people get tripped up by this.

1. Group voting tickets were only abolished 4 federal elections ago, and are bizarrely still a thing here in Victoria and Melbourne City Council. So, people's belief in this is not totally irrational, but likely carried more by lore than facts.
2. Many folks look at elections as a chore rather than a precious gift. They would rather remain ignorant about how they work. "Don't vote for candidate X because they just send their preferences to candidate Y" is more of a meme (in the broad sense of the word) than a well researched political opinion.
3. There are people that benefit from stoking uncertainty and confusion about the Australian election process. Many of them are not Australian citizens. Just look at the AEC's Twitter "Replies" tab. Cookers and Russian agents.

"It’s possible that the mistaken belief comes from How-to-vote cards, or from parties forming coalitions or alliances in parliament."

I'm not sure where this belief comes from either, but I distinctly recall an election campaign many years ago from the Liberal Party, which went along the lines of "A vote for Independents/Greens is a vote for Labor." It was ran late in the campaign before the election and had a definite impact on the election on that occasion, I just can't remember exactly when it was. I wondered at the time how it was even legal.

My mother believed it too. I was more than happy to explain how it works simply to her, like you have here. But she was suspicious about anything I said and I could tell she just simply didn't believe me. People talk about the Murdoch/Sky News/Herald Sun/mainstream news brainwashing nowadays.. it really began a long time ago.