Heh heh. Yeah, it does get confusing.
I joined this site about three years ago. At the time I believed that is was probable that the universe was created by someone who then had nothing further to do with it. I wasn't confident about it but based on what I saw, it seemed quite reasonable. So, I'm an adult, college educated with a BS, and a strong layman's interest in science. It wasn't until I joined this site and had many discussions with people who have discussed this for a long time, that I became a confirmed atheist. In no way do I ever consider even the remote possibility, under any definition of the word, that I was delusional for my belief in God.
My son's girlfriend is studying to be a nurse. She was raised Catholic. She recognizes that her belief in God may be wrong. She has decided that she does not want to examine it further, primarily because she knows if she does so it is possible she may conclude there is no God. From her perspective, she'd rather not take the chance that she might stop believing in God. She likes the thought of God and what that means for her. Her life will be the same whether she believes or not, so she may as well keep that security blanket. Can't say I blame her for that attitude. In no way do I consider her delusional.
I know a lot of theists (I come from a very religious extended family). In no way do I consider any of them delusional. Most of them do not really understand science, and what 'evidence' really means. While they could critically examine their beliefs, it would take a lot of work. Why bother? They already 'know' that God exists. And there aren't that many people around them who would make a concerted effort to challenge them.
So to answer your question "Is the scenario of an individual who is capable of critically examining their belief but doesn't possible?", I say yes, I am confident that not only is it possible, it is widespread.
The people on this site discuss this all the time. They have a strong science background and are well educated. I think many of the atheists here lose touch with average Joe. Challenging one's religious beliefs is, IMO, not something that is widely done in the general population.