Time your SM went back to strata manager school (if they ever attended). Point them in the direction of section 7b of Fair Trading’s Common Property Memorandum which defines what is and isn’t common property:
7. Parking/Garage: (b) electric garage door opener (motor and device) including automatic opening mechanism which serves more than one lot
Sounds like your strata manager is more interested in keeping the committee onside that doing their job properly.