Not sure. I've certainly been asked for my CC during the bag drop process. Did they just quickly swipe it and hand it back to you?

I'd advise the OP to give BA a call. Typically, it could be things like a ticketing problem (if you've changed your booking, the e-ticket(s) may not have been reissued); oversales; aircraft changes etc -the airport sometimes chooses not to release the flight for self service check in for some reason. I guess it's due to "operational reasons"