Channa, the *A agent left a note in the record and told me to tell anyone who looked at it
I certainly believe that they could force me into C if they wanted to. I'm not as confident as you that they would have spent real money on it. I would have expected them to tell me to pound sand, and then Customer Service would give me a few thousand miles.
I called up my old ticket on united.com, and it says I was in classes B-I-B-R for the trip. The first section has already posted as "ZB", so that's correct. The LX segment says "B", and the agent said when checking me in that they had to override the system to issue me a Business boarding pass even though the system thought I was in Economy. However, that BP says C where the Lufthansa one says I. So it's not clear what sort of witchcraft they had to do. A mystery unlikely to be solved.