But I'm still in doubt as to whether the BBC can pull that sort of thing off
The BBC's role in the making of the programme is largely that of a commissioning editor.
That's why the BBC staffer quoted in the story is described as an 'executive' producer - he is managing the independent production company which is actually making the programme.
In other words, the corporation is saying to the film maker: "We will pay you to make the film, and we agree to broadcast it."
There could be some creative tension between the two parties, which may or may not become public.
However, it's likely the production company will have an editorial independence clause in its contract with the BBC.
The BBC article in the OP is carefully written to stress the corporation's complicity in Savile's behaviour, so no one is attempting a whitewash here.
A Newsnight investigation into Savile was halted before completion, which the BBC later apologised for - they couldn't do a lot else by then.
Not that suffocating Newsnight made a great deal of difference.
The story broke on ITV instead, because once again those doing the digging were independent so were able to take what they found out to another broadcaster.
At the heart of that timing was Savile dying.
No doubt he was a big beast for any journalist to tackle, but you (almost) cannot libel the dead, so all bets were off after he carked it.