Unless BA have provided other reports then it's difficult to understand how the CEDR arrived at their conclusion.
For example, what does this mean"The passengers could not certify the credit card and there was no time for them to buy another ticket..." ?
and "it is difficult to believe that no one informed the Passengers the card used to make the booking was required" is not even a definite assertion (let alone a substantiated claim) that such a request was ever made. It appears to be merely the surmise of an interested party,
I'd certainly pursue what more was provided to the CEDR, in particular, you should ask for the PNR to see what instruction was placed in it by BA Security (i.e. whether it contained an explicit requirement to require production of the credit card) and confirmation from the handling agent that they had access to and read the full PNR and then clearly conveyed such requirement to the passenger).
With regard to the above observations about such "Passenger said" vs "BA said" bunfights, I'm not yet sure that we're clear on what BA is even claiming was said...