I've been in the travel business for donkey's years. The issue of transiting without a visa comes up a reasonable number of times, even if it's for a simple UK to Australia on a Chinese airline with a transit in say, Shanghai. It has always, for as long as I can remember, been the case that I will advise travellers that they must be on one through ticket otherwise TWOV (transit without visa) would almost certainly not apply. It was the same during covid when you could still transit a country even though the country itself was off limits. The airline information was that you had to be on one through ticket.
From my perspective the OP has unfortunately fallen into a simple trap that could have been avoided had he spoken with a travel expert who has their hands continually in the suds, but I fully, fully understand that he did all he could beforehand, even involving an immigration expert. I was about to write that the reason for needing one ticket was because of fake onward boarding passes but that has been covered above. I have to side with BA but do hope that they'll recompense him for the genuine error.