I actually have both concerns. I do not think people are typically making a false statement when they say they believe something, even when they clearly have an automatic assessment that does not give it a high probability. But I also think that even if people did make an actual mistake, e.g. by saying “I have a high automatic assessment of this” when they don’t, it probably isn’t very useful or productive to tell them that.
The following two questions are distinct.
Do some people claim to believe things that they don’t “really” believe (whatever exactly we mean by that)?
Should we tell them so?
The rest of what you say seems mostly to be addressing the first question, so I’m not sure why you framed the issue in terms of the second.
I actually have both concerns. I do not think people are typically making a false statement when they say they believe something, even when they clearly have an automatic assessment that does not give it a high probability. But I also think that even if people did make an actual mistake, e.g. by saying “I have a high automatic assessment of this” when they don’t, it probably isn’t very useful or productive to tell them that.