Edited to add: looks like I was beat to the punch on the next page....
If a pax on a full fare fc ticket from lhr to jfk, refused to answer (the more invasive) questions posed by the contract agent, and was denied the sticker, cancelled has flight and got refunded his $9,000 and used a different carrier, like ba, which (it seems) doesn't ask the more invasive questions--how enthused would aa be with the situation?
Magnify this to several such pax, aa would be out "big" bucks.
AA doesn't care if you fly BA or IB across the Atlantic. The three carriers have a JBA and share profits from their operations. Now it's a different story if you choose to do this and fly United, Delta, Virgin, or the likes.