A (or any other airline's) bag tags are useful in one way only. You do not have to put your address on them. It is known to happen that people at airports lurk around to identify a family clearly going on a long vacation and subsequently getting their address of the bag tag. It has happened that baggage handlers have done the same thing.
That is why I tag every bag with a address-less BA tag.
So theoretically, any BAEC member could just put their EC number on their tag, even blues, would this be correct ?