If you look at Whale's response, above, you'll see that the SM is labouring under a common misapprehension. Because the Air-Con was installed by a previous owner without permission doesn't mean that you have to apply to have it on common property – it means that it must now be considered common property and it's up to the OC to maintain it (regardless of who damaged it). The OC at the time it was installed had the opportunity to formalise the arrangement or have it removed. That they didn't do so isn't your fault and they have inherited the issue from the previous OCs.
The other misconception troubling your SM is that the OC doesn't have responsibilty for the actions of their contractors. Why then would they have OH&S insurance, for instance?
All that said, you are now facing a $70 charge if you want to take this to Fair Trading for mediation (an obligatory first step towards a claim at the CTTT. And you might have a smartypants in your EC say, well, if this is common property, let's remove it.
Frankly, I'd be using this as a opportunity to formalise the air-con issue. They can pay the repair bill and for a special resolution by-law to be drawn up whereby you agree to take over the maintenance of the air-con unit in the future. But even if you were responsible for the unit now, they would still be liable for the repairs.
My suggestion – see if you can arrange a free mediation with someone from the Institute of Strata Titles Management who is more across the strata legislation than your guy is. I don't even know if ISTM do mediations but they should.