Thanks for your input guys. They are insistent ! And I am dealing with the BA RTW people in the UK.
However, I managed to re-route the rest of the ticket so as to save a sector on the way into the US. And optimise a few other elements so it works better too. As you say, explaining to someone that they are incorrect and convincing them to accept that is easier said than done. Actually the problem seems to be the fares people, not the agent. Apparently a manager in the fares department (who don't speak directly to customers) told the guy I was speaking to (on the gold executive club line) that he shouldn't be dealing with the ticket because it was too complicated for him. I wonder who it is I am supposed to be speaking to !
I will attack it again the next time I make changes to the ticket. I now have CAI-LHR-IAD-DFW-SYD-WLG-AKL-KUL-CMB-MLE-SGN-DOH//LHR-MCT-DOH-AMM. Lots of miles and tier points there !
By the way, one other thing I was told when trying to make this round of changes was that I can only have three 'Long Segments" in Europe/Middle East. That's why I have DOH/LHR in there as a surface sector. They are saying I can't fly it because I have already done CAI/LHR and I have LHR/MCT later in the ticket. However, that can't be right either, as I did DOH-WAW-DOH-LHR on a previous RTW ticket. Are they also wrong about this ?