While the FOX Network has always taken itself less than seriously, it is easy to see why The Simpsons is allowed such liberty in regards to its clever barbs against its own network.
The Simpsons is the show that made the FOX Network a success. Although FOX has continued to provide some excellent shows since, when The Simpsons premiered FOX was little known and always at the bottom of the ratings heap. The "Big Three" at the time (NBC, CBS and ABC) had constantly battled with one another in the ratings game, but had almost worked out a schedule where each network had a night to call its own, FOX changed all that. Since the debut of The Simpsons FOX has brought on such fan favorites as The X-Files and King of The Hill.
I would suppose that Matt Groening probably has a considerable amount of pull at FOX since Futurama stayed on the air despite an initial ratings disaster (however even The Simpsons took a while to take off).