This makes me think they do in fact have the balance right

Nah, for example Arabs love their coverage of the conflict. It's way more slanted than Reuters for example, and almost as slanted as Al Jazeera.

It's normal for news organizations to be accused of bias in the conflict, as you say, if both parties think that, that's normal.

But BBC has the lovely distinction of also being accused of anti-Semitism, which is a badge of honor that most news organizations have not received.