This is interesting because as I understand it, BA contract G4S at LHR for passport, visa and immigration type verification.
I had a query concerning the validity of a travel document and approached a ticket desk in T5 where the very helpful BA uniformed lady explained how it worked, dialled G4S and handed me the phone to ask the question myself. Received a positive answer immediately.
I wonder why this wasn't checked before denying boarding...or is there more to this perhaps?