Maybe that is the rationale. It's the only thing that'd make sense, but for problem that it doesn't. When somebody, or some entity, lies to you - that entity becomes the liar. People may not want to believe 'the enemy', but that's going to be because of their own ideological reasons, and not because they now refuse to believe anybody. On the contrary non-ideologues may even be ever more swayed towards your enemy as a result of this.

Personally I think the issue is that after WW2 we were left with a large scale and ever growing intelligence apparatus, but with ever fewer appropriate tasks for them. That led directly to the era of recklessly overthrowing nations, often to our own detriment, and gradually transitioned to the modern era of aimless 'information warfare' which I think will ultimately be shown to be very much to our detriment, once again.

This was a great, old anecdote. Until they’ve started the biggest European war of the century.