It's a difficult case as we don't really have any means of knowing whether those push-back restrictions are true or not. But they could very well be. And if the airline knew that a bit in advance, that would explain late boarding and why you just sat there at the gate and waited with the door open (or closed?) for an extended period of time even after boarding was completed.

Unfortunately, I would say that you don't really have a case here as it is difficult to prove the airline wrong.