MCT would not make a difference here, you need to consider SCT - Sensible Connection Time (® Often1). Now if you had left a reasonably long connection, and given the limitations on what Contact Centre can do, the best bet - from quite a number of examples in this forum - is to by all means ring up and ask BA to put a note on the reservation, but don't at that stage rebook the flight. At the BA airport try and get the agents there to see what they can do. This needs to be done with courtesy, compassion may well ensue. Sometimes a free rebooking results, sometimes a modest change fee is charged even though it was a no-show. Now if that didn't work, you can perhaps look at CEDR or MCOL remedies, but the reasonableness will be poked here. If someone left only a short connecion and AA screwed up, then it is actually perhaps more AA on the hook here (Montréal Convention Article 19, good luck with that however) since in making separate reservations you are taking some risk for yourself. Travel insurance may also help. As it happens, your other recourse is that AA are known to intervene here and try to get rebookings, so if your contact is in an Admirals Club, for example, they may also be able to help.

In short, I regard it more of a "best endeavours" policy rather than a firm commitment to get someone out of the mire on each and every occasion. Leaving a short gap between flights involves a chance of delay, that is not beyond the traveller's control, it is a direct choice and risk.