I can't currently find the guest specifications on ba.com, either what you quote or any other rules, but I'm quite sure it used to say on any flight on the same carrier. This has been discussed very extensively on here before, and there has never been a suggestion that it has to be the same flight.

In any case the One World rules, which BA supposedly follow and which the nice dragons at MAD are likely to be more familiar with anyway, are much more lenient and just say the guest has to be on a OW flight.

Edit: Duh! Need to read more carefully. I did actually look at the page to which G-BOAC refers, but didn't read it carefully enough.