An important detail is whether they arrived at the BA counter to talk to the agent a little bit more than one hour before the flight or a little bit less than one hour before the flight, assuming that the BA cutoff for coach passengers (with no bags to check?) at BOS is one hour. How much time did they have between the two flights at BOS and how does this compare to MCT for D-I, AA-BA there?

This is being discussed in the BA forum (you shouldn't double post on FT!), where it's been revealed that it was one ticket issued by Expedia/Priceline/Travelocity and the bag was apparently tagged through to LHR.