BKS - I'll have a go ..., but
When an agent books an itinerary using a GDS it will look to see what flights (nonstop, online, interline) are available. After selecting the flights the customer prefers the GDS will price it. It will look for the lowest possible 'valid' fare. Valid fare means the journey meets all of the various fare conditions attached to a particular fare. Some of the lowest fares restrict the combinability with other fares, or require that the ticket be issued on the 'paper' of the transporting airline. (Why these restrictions may exist is a subject of yet another pricing thread).
BMid and Brymon must have had an interline agreement (likely the IATA Multilateral Interline Traffic Agreement - MITA). So when the GDS finds combinable fares it prices the journey and issues the ticket on one of the two airlines (usually the first). A clever agent may look for a lower combination of non-combinable fares and if that is a better price, will issue two tickets - one on each airline.
In the good old days most airlines would interline baggage (and issue boarding cards; etc) even when two tickets had been issued. The MITA agreement, as a matter of law, only applied when a single ticket (single contract) had been issued, but airline check-in staff weren't bothered by the technicalities. That changed about 10-15 years ago following a dispute between two LHR based airlines. The smaller of the two was having their claims for baggage losses refused by the larger because of dual-ticketing. So the smaller began to refuse baggage from the larger if a single PNR/ticket did not exist. Now, most airlines will not accept interline baggage unless a single ticket/contract exists. There are exceptions of course, for on-line and alliance interline, but you need to be a detective to know who does what.