Any airline has the capability to act as a travel agent and book you any itinerary with competitors. In my life, I have actually physically seen people buying a pure AF ticket at a BA counter, and people buying a pure EK ticket at an AZ counter, although in both cases, I have no idea if it was provocation or genuine habit of buying all their tickets there.

Some airlines may have different fees if you book such a ticket though (as the fee where you buy their own tickets is effectively reduced) but there is no doubt that they have access at all other public airline fares from the PoS.

I'm just puzzled why you would book such a trip through BA rather than through AA or US though?