Check out this NPR story on research showing how people hold inaccurate beliefs even more strongly when presented with contrary evidence. The phenomenon is called "backfire." There is an interview with Prof. Brendan Nyhan, who published on the topic.
The transcript includes discussion by Neal Conan and Dana Milbank about Arizona Governor Jan Brewer, who has been saying all sorts of outlandish and untrue things about immigration and violence.
CONAN: And on Sunday, the Post published a piece you wrote that started with Arizona Governor Jan Brewer's claim that law enforcement agencies found bodies in the desert, either buried or just lying out there, that had been beheaded.
Mr. MILBANK: Yes, I think Governor Brewer lost her head on that one in particular. Now, there's a huge problem with violence on the border, but virtually all of it happens to be on the Mexican side. And what happened in the case of this claim is a news organization out there called the Arizona Guardian called all the coroner's office, the medical examiners in those border counties, and they could not think of a single instance of an immigration-related beheading.
I called the governor's office to see if they could give me some of this decapitation information, and they didn't so much as return an email or a phone call. So I suspect if they had evidence of that, they would have furnished it.
CONAN: And no updates since publication.
Mr. MILBANK: There is no reply still.
I'm pretty sure there never will be.