The trouble is many corporate TAs in the US don't get that the Open Skies agreement means you can use BA (and will be able to after Brexit). They play safe and book US carriers. It sometimes needs a little nudge. The agents get the contracts after promising that any flights they book that are non-compliant will be billed back to them. I feel for the OP.. I've had years of this working for US Govt contractors and a pile of dopey corporate TAs.. One gig, in Turkey, they wanted me to fly from London to JFK, then back to Turkey on a direct flight with United, claiming this was the only compliant route! To avoid the nonsense, I just bought a ticket myself and flew direct.
Many new US Govt contracts now have 'Fly Global'.. you can book what you like.