Can anyone help me with this?

Using the online itinerary planner at oneworld.com I am able to construct the following route with no problems. But when I try to book it (through BA telephone reservations) they claim that there are no direct flights between LAX and BNA and that the only option is to go via DFW (at extra cost and adding extra time). Also they don't recognise the BNA-LGA leg.

Does anyone know why? Is it just that the online planning tool isn't 100% accurate? Or is it that RTW tickets aren't valid on AA1974 or AA1748? Can you only go to major hubs? If so, I can't find anything about this in the fare rules.

Proposed route (this is for business and isn't really flexible on dates or destinations, with the exception of the HKG stopover):

2Feb09 MAN-HKG (BA1399; BA25)
4Feb09 HKG-BNE (QF98)
8Feb09 BNE-SYD (QF529)
11Feb09 SYD-BNA (AA7365; AA1974)
14Feb09 BNA-LGA (AA1748)
20Feb09 JFK-MAN (BA112; BA1384)

Any help gratefully appreciated.

edited to add: this is all in economy.