Danny Baker was not an employee of the BBC either. The show was produced by Campbell Davidson and sold to the BBC. I doubt Carol Thatcher was an "employee" either. They use the term "sacked" so as to couch it in terms the hard of thinking masses can get their heads around. Fact is Danny Baker was a long time critic of the BBC but being the consummate broadcaster that he is, was hard to get rid of. His faux pas with the chimp picture was just the excuse they needed to rid themselves of this troublesome man.
Jo Brand on the other hand represents everything the BBC holds dear. Left as left can be, hating the Tories, hating white men (though the 'white' bit is only inferred, never mentioned). Can't say that i've seen much of her material but from what I have seen I can't help think Jo Brand is like a Paul Calf type character. There's a clever woman in there pretending to be ultra left, right on, dealt a shit hand harridan when she probably votes Tory and Brexit because she's fed up paying too much tax to fund the feckless foreigners that are lowering the tone of Richmond on Thames.