Being in the same situation where my long-haired general requires visas for multiple destinations where I don’t, I feel your pain on this one although luckily never been in the same situation of IDB (albeit waiting in angst to hear check-in completed on several occasions). Funnily the last one where she was transiting in JNB to get our onward flight 36 hours later. She has a visa however there is a note on it that she must hold a return ticket. I was concerned that my interpretation may differ from the airline bringing her into RSA would differ from mine as technically her return ticket started in JNB back to FIH. I armed her with every letter, copies of my passport, hotel booking and flight but none were asked for at check-in at her departure point and on arrival in JNB, the immigration officer didn’t even ask her how long she was there for or proof of where she was staying. Stamped passport and welcome to South Africa.

I always make sure the boss is at the airport in plenty of time (no chance of her travelling HBO ) to ensure any additional checks, conversations, etc. can be done without taking check-in and clearing security and immigration down to the wire. Had your wife been at check in earlier and the issue came to light, I don’t think it could have been beyond the realms that BA LHR could have possibly have attempted to contact their counterparts at JNB to check with RSA immigration as there were BA flights operating around the same time. Just a thought outside the box.

Hope you get something sorted out quickly.