"They think she is smart"
I don't think that is really it. She's "got her mind right" so they excuse her stupidity. With that bunch, you don't have to be smart, you just have to want to return the government to conservative control.
In that respect she sees the world like Rush Limbaugh, only she's female and attractive rather than fat, male, and balding. She's one of them. She was really set up by her speech at the RNC. It was clearly written by someone else because it was far too coherent to be her writing, but it matched her tone perfectly. I can't decide if the McCain campaign decision to write her speech in that tone was brilliant or horribly misguided. I do know that up to that point she was an interesting anomaly to me, and after that speech I felt nothing but revulsion for her. I also know McCain lost the election. That speech resonated powerfully with the teabagger crowd and she has coasted on it ever since, but it also placed her squarely in their camp, and that limits her electability, you might even say it cripples it.