When you say CX-booked, do you mean an award flight using CX FF miles? And usually this "double-dipping" issue only is a problem if one is trying to get a complimentary upgrade when technically they shouldn't. Because there are people who are AA elites (and also OWS/OWE with BA) who book, ticket, and get upgraded as AA elites on an AA domestic flight, and then show up at the AC/FL with their BAEC card, and are let in. And I think this is not a problem in their eyes because AA gets re-imbursed by BA for that entry.

On the other hand, if that same person books a flight on AA but uses their BAEC number so it credits to BA, and then tries to enter their AA FF number in order to score a complimentary upgrade, that's the red line that they tend to draw in the sand. More so, because BA isn't going to give AA any money for that upgraded seat, while AA has to pay BA for the FF miles being credited into that BAEC account..