I wonder if this equates to those people who seem to be able to know what you are thinking- those who tell you about yourself in a way that's both abrupt and jarring- as if the idea that you were somehow concealed was made ludicrous. Or maybe those whose advice seems to casually key into a part of yourself you didn't even know was legible from the outside.
There's people who can also read into the heart of situations. Alexander the Great was said to be a master of war both for his swift action and reaction in battle as well as his ability to make sudden decisions based on a swift understanding of the situation as it was happening. He could change plays...mid-play...because he was able to see what was happening and what needed to be done.
Aren't these things like real-life super-powers in a way? They are definitely valuable ones, but they also fill those who do not possess them with a sense of awe. Kind of like watching parkour, we never imagined some things as possible until we actually see it and even when we do, if it remains far beyond our personal concept of possible, it's somewhat mystical in a way. You could also consider the woman who lifted a car off her baby. In fiction we call this, in general, a body enhancement technique- something that amplifies physical strength to wildly unnatural...or atypical...levels. But it happened in real life.
What I'm saying is that there seems to be three categories. The definite, the quasi-supernatural (or misunderstood), and the supernatural. As time goes by we find that some things that we once thought of as supernatural is natural. It simply wasn't understood. For instance...what if telepathy wasn't telepathy in the supernatural sense. What if it's an unconscious sensing of things like micro and macroexpressions of the body. But not only that... What if one body could read the subtle fluctuations of heat or electrical impulses in another body? Or what if Our bodies were carrying on a secret communication using subtle signals like smell and chemical messaging that our conscious minds weren't aware of? (like pheromones) As you can see, its not exactly the same thing as reading a persons mind, but it comes close if we believe that our emotions result in fairly consistent reactions from the body.
In terms of fictional writing there is definitely a place for all of this... If nothing else, I like the vagueness of possible and impossible. The way faults in perception always bring into question our understanding of our reality or the entire story. It's kind of like if Jesus really did come back. If he did...then what is science? If Jesus came back...is science invalid, or is our understanding of science even more woefully inept than we thought it was? Because the very existence of a thing like Jesus would force us all to question everything we've been told. Believe or not, we all live by a scientific method of sorts. A tactile method for a tactile existence. But what if, one day, you found fairies living in your tree? Not every tree. Maybe not even any other tree. But still, you found them. And you can show them to others. They are undeniable proof of something that contradicts established sense.