Yes, that is IDB - you presented yourself for check-in with valid documents, you are not allowed to board and the aircraft leaves without you. Unfortunately BA's system tend to say flights are cancelled, without adding to two important words "for you". Or perhaps "for youse". It's possible the agent was just going off their screen, and therefore didn't know it was just overbooked, but that seems somewhat far-fetched. They probably didn't want to prolong any discussion of this. I would claim all your costs and IDB for each passenger. It may be one that BA won't fight because it will be clear it was an overbooking, and they needed a group of 4 off so they could seat other children with parents / disabled passengers.