I think OP should at least try to claim IDB.

Just dont be an "I'll sue you" douche or you just might get a "go right ahead" response, and then who knows if you'll win in the end.

Explain the facts, be clear about the times, and attach a picture of the boarding gate with you there. Make sure to say you were taken off the flight by some automated system, but still made the original flight for which you were told "sorry, it's full".