Towards the end of my time in the mental prison of JWdom, one of the few remaining threads that my loyalty to the cult was hanging by was the fact that one of the elders in my congregation was very intelligent and often gave comments about how he had previously been agnostic before converting. I liked him personally, and I couldn't understand how he wouldn't be able to see all the issues that I could see. But he was still in and by all accounts fully invested.
One day I was bored and thinking about this predicament and googled "Why do smart people believe stupid things" which lead me to an article that referenced Festinger's "When Prophecy Fails" - a well regarded book written after following around a doomsday cult to study the psychology of it all. I never actually read the book, but the overview on wikipedia hit me pretty hard. In a lot of ways it sounded like the JWs - they predicted the end of the world, and after the failure of the prediction the ones that stuck around were more committed than ever and this is when they began to attempt to proselytize. When you're uncertain of a belief that you hold, convincing others of its truth validates the belief to you, so you seek to do that. I'm not saying that's exactly what happened with JWs, but at the time I didn't know fully the history, but I knew the preaching work mainly started after 1914.
In short, intelligence has less to do with whether you believe stupid things than we'd like to think. In many cases it has much more to do with how invested you are in the truth of an idea. If you've given up jobs, family, friendships, property or a great deal of time in commitment to it, you're far more likely to continue to hold this to be true long after it's proven false. In the case of the elder I'd looked up to, he'd given up all these things for the cult. I also later learned that he converted only after his wife had converted, and this lent further credence to the idea that he, in spite of his intelligence, may well have been fooled into holding some very stupid beliefs.