BA did even more than that for me a few years back - much more. I got off an overnight trans-Atlantic, and accidentally left my toiletries bag in the underseat drawer. I only discovered this when I was in the Arrivals Lounge shower. I went to the desk and asked the dragon what could be done. After she'd clarified that it was my own toiletries bag (with my medication in it), and not the free amenity kit, she made a phone call which included the helpful sentence "And he's a Gold card holder too."
It took a little over an hour, but someone got in a car, drove over to the maintenance base to which the aircraft had already been towed, retrieved the bag, and drove it back over to T5 to hand it to me in the lounge.
It's the sort of event which makes you forgive a lot of the small wrinkles that happen in everyday flying.