Interesting why folks will cling so tenaciously to incorrect ideas. Anyone read "Thinking, Fast and Slow" by Amos Tversky and Daniel Kahneman? I read a good portion of it last fall. I've gotta imagine that the ability of the Game Show problem to stump PHD's is a result of some form of common cognitive bias. I don't have the time to look it up right now, but I'd figure that Tversky and Kahneman may have something to say about it as well.
My best guess is pride in two different ways. First it leads to arrogance, which is when someone boldly claims that they are correct and the other person is an idiot. Second, that person will try to protect their pride by working to remain ignorant of the fact that said "idiot" is actually correct. People spend a lot of energy protecting their ego and pride by doing things that don't make sense.