A common logical flaw

There is a letter in this week's Spectator that contains a common logical flaw that supporters of the BBC like to use as proof  that the BBC is not biased. Here's the two key sentences:

'On the touchstone issue of the Middle East for example, both the supporters of the Israelis and the Palestinians claim that the BBC favours their enemies. This would seem to suggest that its attempt to chart a middle course through some notoriously difficult territory is at least partially succesful'

Several thoughts come to mind, here's one: there is not necessarily a middle ground between good and evil, would Jon Stubbings have agreed with the BBC charting a middle course between Nazism and freedom during the Second World War? Would the BBC have been biased had it not seen the Nazi regime's point of view? Just because the BBC is criticised by both sides of an argument does not mean they are steering a middle course. Israel's position is that the Palestinians deserve a state but a state that lives in peace alongside Israel, Hams and Fatah's positions is that the end game is the destruction of Israel as a Jewish entity and in
Hamas's case also the killing of all Jews. Between those two extremes maybe the BBC does 'chart a middle course' but are the two sides' positions equally valid?

Jon Subbings' letter concludes with another logical flaw:

'Given a choice between the BBC with all its faults, and a broadcast media dominated by the Murdochs or a Silvio Berlusconi figure, I know which I would prefer'

Quite possibly you do, but at present I am forced to pay for the BBC's output and not for Sky and so I should be able to expect an unbiased BBC.