To be fair to BA they do sometimes do this. The only time my bag went missing I was met at the bottom of the jet bridge by a gentleman who informed me my bag hadn't made it, he then helped me through form filling, gave me a preloaded cash card and walked me through the diplomats lane at passport control.

This was at Narita, so maybe Japanese efficiency.

I'd much rather have had my case but it certainly helped to have this service.