Regardless of pedantic definitions, and speaking morally, did you use their services?
Short answer - No. I did make use of Perth Centre's radar services and the RNAV approach, for which I would have already been billed through ASA's navigation charges.
Would you have been there if there wasn't an airport?
Interesting question. Should I be billed for each airport that I fly over, just because they happen to be there, as a convenient waypoint?
It costs them money to provide that airport, if you approach it and subsequently go around, you have still "used" it, no? It's not like a "landing fee" is used only to cover wear and tear on the runway.
What else is a landing fee if not just that? Your argument would hold if they had called it a "user fee", and I would have no argument with that.