Thanks for all the replies.

I rang up Qantas just to see their interpretation of the rules and they have told me the same thing as the travel agent. They even gave me an example of flying into LGA and out of JFK counts as an additional segment.

So are both the travel agent and Qantas wrong?

The travel agent also seems to be unable to ticket it as an 001 ticket and has to ticket it as an 081. My understanding is that an 001 ticket will have less fuel fines... what would be the difference in price? My full itinerary is:
SYD-SFO/SJC-ORD-YYZ/YVR-DFW-YYZ-ORD-CDG-LHR-MUC-LHR-FRA-NRT-SYD with QF flight numbers where possible.