I agree that it's entirely up to the OP whether to take the matter further and I can completely understand why they may decide they have better things to do. But equally airlines get away with this because they are not challenged on the whole, and even when a challenge is successful the airlines only change behaviour if it costs them money.

Now did you notice how they referred to a "valid ticket"? Let us have a look at the actual wording: " "reservation" means the fact that the passenger has a ticket, or other proof, which indicates that the reservation has been accepted and registered by the air carrier or tour operator;" Now you can see the second clause there, "other proof". It's just a bit curious that they did not mention the "other proof" bit, which presumably you have. Nor have BA mentioned the "high level of protection" aspects in the preamble.

Now any submission to CEDR needs to be carefully worded, but for now, yes, just send a single sentence, nothing else at all, to get what is in effect a deadlock letter from BA.