Alas, I very specifically wanted to book with BA because I have vouchers I needed to use!
The very helpful lady on the Gold Line (after 1hr of waiting) found that BA's system was also pushing through BA's J fares, when Matrix was giving I.....but in the end we did DUB -> PHL -> LAS -> JFK -> LHR -> DUB for just over £1,300. Would have been less booking with AA - but never mind!
It's become an issue for me searching ITA for only BA ticketed flights - when often AA offer cheaper ones, etc. Good news is vouchers are spent! So that takes me to the free market next time!