This used to be a bigger deal in the past (10+ years ago) than it seems to be now. I have been in this situation a few times when (1) the card used to purchase the ticket had expired by the time I took the flight, and (2) I bought a ticket for someone else who was flying from a different origin airport, or just flying without me. What I did was to call BA well before the flight in question to explain the situation and have the information added to the record. After doing that I never had an issue that resulted in a missed flight, although there were a few instances of the check-in agent actually asking for the card and then having to read the record.