I can only make sense of the left's belief that the BBC is right wing in one way:
Left = "There is only one right opinion. And it is mine."
Right = "Everyone has their own opinion. I just disagree with yours."
That is the only way that for example I can reconcile the evidence of BBC Question Time having two thirds of panellists being Remainers, and thus upsetting right-wing Brexiteers, and them having any Leaver panellists, and thus upsetting left-wing Remainers. (I don't know what left-wing Brexiteers or right-wing Remainers think about this.)