As I understand the sentence quoted, I disagree with the author.
All the versions are valid and have different meanings.
- I would have liked to see Australia.
When I was younger, to see Australia is what I would have liked. Now that I'm older, it isn't what I would like because I don't like long plane journeys.
- I would like to have seen Australia.
I would like now to have seen Australia in the past.
- I would have liked to have seen Australia.
My memory is failing but I'm pretty sure that, when I was 30, I would at that time have liked to have seen Australia when I was 20.
In real life, people don't make these distinctions and you will hear all three versions. What people usually mean is, "I wish I'd visited Australia when I was younger"