I called to try book a flight from ZRH to PHL via LHR and JFK in Club World. Funny the agent said after I read him the exact flight numbers:

"Sir, are you trying to cheat the system for more TPs?? You know we have a direct flight to PHL from London"

I replied:
"Are you saying what you are saying? I am cheating the system? You have 2 flights to PHL. I am calling because through google flights I can get it to price up on AA but for BA google saids call BA. Have you ever thought of the idea of someone who might want upgrade with Avios and the availability of that? If you are unable to help that's fine I can hang up."

So he did go ahead (or pretended to ) and price it up, the quote ended up twice as much as AA. Needless to say I just booked with AA and kept my points.

Very cheeky and unprofessional customer service. I've had very helpful and knowledgeable CS agent in the pass when calling the gold line. But this is what I got from calling the number read off google.