I had the very same discussion with a LH ground agent last year when my HAM-MUC morning flight was delayed: I got up, checked my flight status, saw a 3h delay and called LH FTL Hotline. They confirmed that the flight was delayed, checked me in and asked me to be at the airport 2.5h. I was there on time, the ticket machine denied to print my boarding pass and when I approached the counter the ground agent told me the very same thing: that they cancelled my check-in (I was wondering: on what grounds can they possibly do such a thing) and that they gave my seat away to a standby passenger. I was very lucky that the hotline girl hat put a call record of what we had discussed on the system: when I insisted that I had called and that I was only following LH issued instructions the ground agent read this note on her system that I has indeed called and sighingly assigned me a boarding pass.

Since then I have sworn to myself to always tell the hotline staff to put a note on the system registering my call and any agreement.