This seems to be a common line of enquiry on sites like this - where someone decides what BA (/any organisation) might reasonably want to do and so assumes that is therefore the correct (and legal) thing to do.

I think we can all see why BA wouldn't want to take a risk where someone is connecting on separate tickets in a country where they aren't permitted entry, the actual question that needs answering however is does BA actually have the right to choose not to take that risk.

With the usual caveat of me not being a lawyer, none of the conditions of carriage quoted seem to give them that right. A clause saying something like "you must have the correct visa/documentation to enter the final destination stated on your BA ticket/itinerary" would be very reasonable to include, but if it's not there, how can you argue they can simply decide that on the day?