O'Reilly gets paid to rake muck, not make jokes. Making joke and showing a clip doesn't fit the formula of Bill's show, and it never has. What does fit his formula is overreacting to something that goes against his or his show's established moral code. He's smiling because he is trying to keep a cool head about it, but it's pretty clear from his history that O'Reilly thinks the joke is in poor taste. Which is sad, because it is really funny, and Fox should be able to laugh at himself.
Let's not forget, Bill O'Reilly regularly represents the views and opinions of an entire generation of Americans who thought Bart Simpson was going to corrupt our nation's youth simply by talking back to his parents. It was on the documentary about the Simpsons; before Family Guy, South Park, et. al., the Simpsons was one of the culturally edgiest shows out there, and people took offense to it left and right.
I don't think Elizabeth meant he literally believes the characters are real; she's hyperbolizing. It strikes me as a good writing technique, because all Fox news does is over-exaggerate and sensationalize stories that aren't worthy of the attention, so making fun of them in that manner only seems appropriate.