It's possible my original dealer did change the battery in the key I gave them for the 2-year service. I have no way of knowing, as that's the key that subsequently had the accident. They never asked me for the other key though.
Central Garage obviously didn't change the battery in the key they had (the one the original dealer never had) for the 3-year service, because I got the low battery warning a few days later. However, if the battery-replacement thing is only supposed to happen every two years, he wouldn't have been expected to.
I did ask him for the price of a replacement for the faulty key, and it wasn't too bad because I still had the emergency mechanical key, and he said that was the really expensive part. But as he said, if the key works normally for three days if you put a new battery in it, it still functions as a spare key, so why bother?