No, the licence fee is guaranteed but that is not the entirety of the BBC's income. BBC Worldwide is a commercial outfit that makes the Beeb a pile of cash that is re-invested in UK broadcasting. That commercial income is just as sensitive to a recession as any other business. The BBC is not nearly as exposed as its competitors, but to suggest it is immune is pretty wide of the mark.
More details here:
http://www.guardian.co.uk/media/2009...moyles-pay-cut