Bottom line, you were late at check in and had a restricted ticket. They tried to accommodate you but it would have meant leaving the baggage.
If your complaint is you were denied boarding then you need to take take it up with AA but on the basis that you arrived 15 mins after check in closed then I can't see you having much luck.
If your complaint is you didn't get your miles refunded then that is normally the case with promo tickets when you miss the flight. Sometimes you strike it lucky with a sympathetic agent but not guaranteed. It sounds like they made a gesture (30,000 miles) which I suspect normal (non GGL) travellers might not have got.
I can't see any breach of trust here by BA. Maybe if you regularly cut it fine, as you suggest, then either setting off earlier or buying a flexible ticket might be the best approach.