OK, you appear to know this stuff. But I am surprised. I would think that

(a) AA might have access to BA's computer system to enter the numbers, even if they are separate reservations;

(b) BA's computers might take an item that has been interlined, and figure out from the tag data that it belongs to an actual passenger who has boarded or is expected to board;

(c) If neither of these things are possible, AA shouldn't interline bags the way they do (it can't be only the UK that has a strict luggage matching policy---I am aware that the US does not, but what about Europe, Asia...?)

(d) If AA is continuing to blithely send bags through that won't get on the connecting flight, one would think that this might be a major issue discussed on FT. I haven't read every thread here, so maybe I missed it, but I have never heard of this problem before. Does everyone with two separate bookings lose luggage if they don't check in with BA?