Robert, you are right that BBC receives criticism from both sides, and it is of course within its charter to remain objective, not to take sides.
However I disagree with your assertion that BBC is 'not part of the problem'. The fact is that a very latrge number of english people, including many politicians (judging by their Westminster statements) rely on the BBC to inform their judgement.
Lyse Doucet's assertion (on twitter) that everyone already knows the wider context - with the implication that in her program she had no obligation to mention e.g. the occupation, the daily ceasefire violations, administrative detentions, the *killings* before and after OPE, or explain even the slightest aspect of the wider context - is patently untrue.
Her program represents a very moving, very skillful framing of the 3rd Gaza Massacre as conflict of two equal sides. The closing caption of the program, invoking the cynical explanation of 'self-defence in response to rockets' message - the same cheap talking point rolled out in Westminster time and again, was simply shameful.