One other thing I have noticed, reading the email from BA more closely is the second line. I don't recall ever seeing that before. Has it always been there? I had assumed it was impossible for BA to assign a seat but possibly they can request one like a travel agent.

"This is your e-ticket receipt. Your ticket is held in our systems, you will not receive a paper ticket for your booking.
If your itinerary includes an American Airlines flight, we recommend you contact us to pre-assign seats.
If the payment cardholder is travelling, you must bring the card used to pay for this booking to the airport with you, for verification, before you can travel."