It makes more sense if you notice that the facts they're rebelling against are also things most people "don't actually believe ... but just say they do." Humans hold all sorts of crazy far-mode beliefs (especially about religion and morality) that completely fail to influence how they react to situations in their day-to-day lives.

Unless you're a member of the space program or know someone who is, whether the moon landing happened or didn't won't change your predictions about anything else. And precisely because of this, it's something that can be debated on either side to signal allegiance to some greater ideal.