In the spirit of helping to return this thread to information and discussion:

If you were on two separate tickets, you were not on a through ticket.

No, you need to make sure you are booked on a through ticket (ie you have one ticket for all the sectors of your journey). This may cost you a bit more, because some of the cheapest fares cannot be combined with other fares on the same ticket. Hence you have to decide whether to trade the convenience of a true through-journey (including through-checked bags) against the cost saving of getting two separate tickets.

In addition, IIRC BA will still through-check your bags if you connect from BA to BA, or BA to another oneworld carrier, on two separate tickets. So you can keep the cost savings so long as you pick your airlines appropriately.

As for the information about connecting flights, each of the airlines may well know about them because they can be input as additional information in the reservations, or sometimes even get automatically communicated by the TA's GDS, even though the connections are not ticketed on the same ticket.

BTW, in case you're still wondering about the rationale for the BA policy, one of the things that has been happening more and more frequently is travellers booking their connections on two separate tickets not just to get the cheaper fares, but also to circumvent a minimum connecting time requirement. Inevitably, if people do that, there is a much increased chance that baggage will misconnect. Guess who ends up lumbered with the cost of sorting that out? I think that you'll find that it costs more than $20 a bag to reunited a late bag with a passenger.

[Edited to add:]

FWIW, there is unlikely to be any way to stop the spread of this policy, which is after all based on sound commercial sense. I notice that bmi (a full Star Alliance member) is adopting this policy, which is stricter than BA's:-