About to start an ex-CAI, my first RTW - thank you Central Bank of Egypt!

I booked a boilerplate DONE4 itin that worked on the OW tool, and plated that with the BA GGL team on 125 stock to lock in the low price.
Whilst the crazy low pricing was still available, I asked BA to quote a new, better optimised itinerary, but their rates desk said the itinerary didn't meet the requirements. I did two rounds of this before putting it on the backburner; now picking this up again as I will soon fly the first segment and I will be able to change using historical fares.
Routing 1 CAI-LHR-SIN-NRT-BLR-SYDxTBU-SYD-JFK-MEX-JFKxLAX-DOHxBCN-DOHxSEZ-DOH (changing the DONE4 into DONE5, by adding Africa)
BA's rates desk responded:
On a round-the-world fare, you must move sequentially around the continents, you cannot exit a continent and then fly back into it again the way you have requested with your flights between Doha and the Seychelles.
Routing 2 CAI-LHR-SIN-NRT-BLR-SYDxTBU-SYD-JFK-MEX-JFKxLAX-DOHxBCN-DOH (keeping at DONE4)
In this case BA told me that the itin was not valid according to the OW tool, and left it at that.
Is the BA rates desk correct, or are they missing the plot?