The question in my mind is if they forged the evidence or if due to some operational glitch, the gate folks thought that you checked in later than you actually did.
That would explain why they denied boarding and ended up going to court over it rather than just settling.
I subscribe to the theory that the simpliest solution is the most likely. They probably made a mistake and thought you were late and then a crazy nut for going after them for compensation.
Interesting story, though. Airlines go to court more often over these sorts of things than broken seats, I suspect. There's some total nut that has a web site devoted to a similar incident with Continental. He's really lost it, though.