So, I made a booking through the AA RTW desk, but the agent told me that the Rates desk might reject it as it doesn't contain any AA flights.

This is despite me telling them that the first leg (SIN-HKG) is an AA codeshare even though the plane belongs to CX. Is there any way around this? The itinerary they have sent me shows the carrier as CX. This whole process is getting quite frustrating.