Despite the fact that it airs on the network, The Simpsons has never been shy of poking fun at the company. In fairness to Fox they've never interfered too much, and certainly given the writers the freedom to make these jokes. Still, they'd surely rather you think they were in on the joke, rather than being the butt of so many, and indeed all with differing variations.
Over the years the jokes have ranged from being about Fox as a young network with little to offer, to then having a slew of terrible programming, and even taking major jabs at the right-wing nature of Fox News.
These even go as far as to include gags around Rupert Murdoch, who has appeared on the show, making him sign his name out in crayon while Homer spelled it for him, and a Fox News helicopter reading: "Not Racist, But #1 With Racists." Of course, The Simpsons has long been Fox's biggest cash cow, so they can get away with it, plus there's a lot of truth in what they're saying anyway.