I think your stretching to make fun of O'Reilly here. He's not my favorite guy in the world (despite being pretty right wing) but I easily understood what he was saying.
I think his point was that Fox is not holding it's cartoonists to any standards, and that if he blasted his bosses on the air like that, he'd be fired. I can see his point.
I can get that Fox's animated shows are largely done by liberals, and Fox, or at least the news portion, doesn't lean as far left as they would like. There are still things they shouldn't be doing.
To put it bluntly if I worked there, and the guys doing "The Simpsons" did that without someone being fired, I'd be POed myself. That's like a guy from another department insulting you on the billboard or whatever, except this isn't even just "in house" it's in front of a national audience. Whether you agree with what is being said in the cartoon here (and don't like Fox News) that isn't really what this is about. If I worked for these guys and someone did something like that, and my bosses didn't do something about it, I'd be pretty POed. "Joke" aside, it would tell me I wasn't valued. If I'm getting O'Reilly's response here I don't think this was something the Fox News team was "in" on.