I recall reading in the other thread on this topic that BA told their ground staff it was a CAA requirement, but a journalist asked the CAA about it and they said no it's not our requirement, it's entirely BA policy.

Ignoring that and assuming it really is a CAA requirement to confirm the ID presented at bag drop matches the ID presented at the gate, then BA's approach is still regularly failing to do this under their new policy, based on the reports in both threads.