Thanks so much for the thoughtful comments, orbitmic!

I had not known that at LHR one may be denied boarding if some system thinks that their arrival at security will or will not allow them to make their flight. In the US you are simply let through security.

I hear that I should book linked tickets or longer connection times, but travel plans change. It wasn't just us affected but several other travelers.

It worries me that even if I'm on one itinerary there is an additional factor that determines whether I'll be let on my flight or not. Is there anything that the airlines do to educate consumers? Based on this episode I'll probably stick with nonstops and avoid LHR and all the associated drama/confusion.