I've never seen any indication that they do. It seems to be all that they can do to keep up with their own issued cards.
That's just my guess though; interesting question. The problem would be that they could presumably follow your purchases, but they wouldn't know how you pay, other than by comparing the transactions to your payments on co-branded AmEx cards that they see on their soft inquires. And I don't even know if they are able to record your non-AmEx AmEx purchases, so to speak.
Hmm, I enjoy a good conspiracy theory as much as anyone, but I'm thinking that although this is technically possible, they have neither the time nor manpower to do so.
* Credit is a wonderful servant, but a terrible master. * Who's the boss --you or your credit?
FICO's: EQ 781 - TU 793 - EX 779 (from PSECU) - Done credit hunting; having fun with credit gardening. - EQ 590 on 5/14/2007