Yes, I think it's something like that. People have an experience--for a moment let's not worry about the cause or source. They have a real experience, a truly ineffable and usually life-changing spiritual experience. It usually involves a feeling of peace and well-being and a sense of connection, either to the universe or God or both. Then they have to incorporate it into their understanding so far. If they have a religious framework, they experience it in those terms. It doesn't mean it's bogus, but that they can only grasp or even experience it, or understand their experience, in terms of their prior concepts.
Oh, another thing. The experience is accompanied by a sensation of absolute certainty. So whatever they experience, post-filter, they are completely convinced of, and nothing you can say can dissuade them. So a Mormon will say that they know for a fact the holy spirit exists, but they cannot convey the experience to you. A Catholic may say they have experienced the Virgin Mary directly, and so forth.
One possible explanation (not the only one, for sure) is that there is a divine presence, that either only visits a few people or only a few people are able to perceive and only occasionally, and that each person understands that presence in terms they can understand.