I would have thought that BA's gate system would have prevented a person with the wrong ticket from boarding the wrong aircraft. Therefore, I'll suggest this gentlemen and his wife went to the destination on their tickets. Which means he purchased a tickets for somewhere they didn't want to go. Therefore, they were sold by someone who may not have done their job properly. I would have thought a good ticket agent would not only have have confirmed the destination country but also in passing, ask what the traveller intended to do on arrival. Even if just to book a hotel, sell some currency or arrange an excursion. You would also have thought that a "professional" person would have put the cost and flight time through their own "credibility filter" and smelt something wrong. Or would this be the sort of dentist who looks in the wrong hole for somebody's teeth?
I've also seen similar in Europe. People thinking that their flight to Kristiansund was shorter than they expected, only to find they were a few miles short in Kristiansand. People arriving in Sandefjord and asking how they catch the bus to Olso, not realising that real airlines fly direct. Americans doing DIY flight itineraries, arriving at Gatwick and departing from that other well known London airport in Luton (at least they weren't in the London in Ontario).
Returning to the dentist, if I were BA, I'd tell him to go away.