I think that's quite a separate scenario though - here, you were flying on IB and had a separate booking (self-transfer) booked on BA. In that case, there is no difficulty for most airline systems to actually connect the two PNRs (something airlines which through check bags on separate itineraries do routinely) to issue a luggage tag and/or BPs for both (though usually, they will then not be able to change your seat for instance, just print the BP).

What the OP is asking is different, it is about going to ask an airline with whom you are not flying at all to print your BP for some competitor. I am not aware of any airline which would do that, and suspect, as others upthread, that the Pristina example is precisely one of the check in agent approached working for the subcontractor which fortuitously happens to work for BA too, and therefore having access to both systems. They obviously did not have to do this if check in was not open for the BA flight, but the point is that whether they were putting a BA jacket or a LH or AF one, they were still the same people and had access to all the relevant systems of the airlines they represented at the airport.