Because of the double absurdity of the situation.
Stewie and Chris were lost in the woods. They didn't think they would make it out alive. Chris mused about what he would do if they "could only make it out alive," and that was finally approaching a girl he liked.
When they eventually made it out of the woods alive, Stewie held Chris to his word. And it turns out the girl wasn't who we might imagine her to be (e.g., the popular chick, the hot chick, the girl-next-door type) . . . she was a girl with Down Syndrome.
Absurd.
But then sweet, when you realize Chris might actually have a crush on someone worth having a crush on---despite the fact that she might not fit the traditional stereotype. So then, once they've established that, and Chris approaches her, and they agree to go out on a date, we, the audience, find out that she's not sweet at all, like we, the audience, might imagine someone in her situation to be, but a raging bitch.
Absurd, part two.
The reference to the former governor of Alaska was a simple throw-away line, and didn't contribute at all to the thread of the bit. Kind of like how Brian has a Kucinich sticker on his Prius.
Palin's reaction to this proves she's absolutely tone deaf . . . probably didn't even watch the episode, but reacted to someone telling her about it.
This is something that the Farrelly Brothers do a lot. They do a lot of work with different groups for the disabled and they cast a lot of disabled people in their movies. And they often have them playing real jerks.
I like this approach. Too often, disabled people are portrayed as some kind of angel who are only here to remind us how lucky we are. I like making them 3D people who can be just as nasty as anyone else.