The bit about leaving your bags unattended is definitely incorrect, you are responsible for your bags in LHR, see Heathrow 2014 Bylaws 3.9. And an agent suggesting you breach the bylaws is in turn in breach of their conditions of employment.
Double yellow is required to be fully investigated though, the requirement is that HAL security is certain that you are safe for passage, and it is ultimately in everyone's best interest. Doesn't excuse incompetent handling though.