Here's what I think. Belief is an involuntary faculty. You can't force yourself to believe or unbelieve something. Our belief is dictated to us against our will, by compelling facts and evidence. If you see clear facts or evidence pointing to a particular conclusion, you can't help but believe the conclusion is true.
What a person can do - and what I believe JWs do - is enter into a state of denial and suppress the inconvenient beliefs that the facts suggest. So its not that they don't believe - it's that they're suppressing the belief. A person can pretend to them self that their suppressed belief is not true and pretend to believe the contrary. But deep down, they actually believe what the facts suggest. They're just not prepared to accept and embrace the suppressed belief because the implications of doing so are painful in some way.
For example, fear of missing out on paradise or being destroyed at Armageddon for disloyalty to Jehovah's organization; or maybe the pride that has built up from the egotistical notion of belonging to the only true religion, may motivate JWs to suppress their belief that their organization is wrong, when confronted with compelling facts and evidence.
This is why they experience cognitive dissonance and is the reason why the organization coaches JWs to practice self-censorship and avoid apostate sites and information critical of the organization. Because right up to the top level of the organization - especially at the top level of the organization - they already believe deep down, that many of their teachings are false and that Jesus didn't really choose the GB in 1919.
They already believe this but they are suppressing that inconvenient belief because of the unpleasant implications of accepting it. And it is precisely because they already believe it and are suppressing it, that they project their own efforts to suppress the belief unto the rank and file publishers by telling them not to visit apostate sites and not to think independently. They are projecting their own battle with cognitive dissonance unto the rank and file. They know there is compelling, irrefutable evidence on apostate sites that disprove the organization.