There are threads here on FT about a much simpler and more cut & dry situation. The pax for one reason or another has an internal ticket XXX-LHR, e.g. MAN-LHR. He then has another ticket for a long-haul, LHR-YYY, e.g. LHR-HKG. The first flight is delayed such that the pax misses the long-haul and due to ticket fare rules is told that he must buy a new ticket as BA satisfied its contract by getting the pax to LHR albeit late.
The examples of BA simply allowing the pax to fly an xEU, commencing at LHR, having nothing to do with fault are luck.
It is wholly unclear to me whether a carrier handling this situation online, e.g. BA-BA, applies its own rules or those of OW which might -- and I stress might -- only apply to offline, e.g. OW-BA or BA-OW.