Indeed and the way airlines work is that while Montréal in essence says that they, the airlines, can get costs covered by the fault airline, in day to day reality it's always the final airline that resolves this to customers. In practical terms it can be no other solution. Imagine this was a trip to a regional airport in Mexico, one with no BA representation, and imagine the OP was a Mexico resident - telling them to go after BA would be a hopeless approach. Ditto on the return leg, had someone based in EDI found that someone in Mexico for AM had delayed a bag, telling that passenger to liaise with AM would not be helpful, but making BA the focal point makes a lot of sense. Though all large airlines now like to centralise the task, in theory there is a baggage agent at each airport charged with the monitoring and recovery of bags and replacing contents. Smaller airlines such as Loganair still do this.