I think that it can only be taught, or at least only be learned.
What does it mean to have a 'personal' and 'unique' vision?
As to "personal," every person's vision is inherently, by definition, personal. Even if someone is a hack who just goes out with a camera to consciously copy Ansel Adams (shudder), they are still personally ripping off Ansel Adams.
"Unique," on the other hand, is an entirely different can of worms. For something to be unique, it has to be "existing as the only one or as the sole example; single; solitary in type or characteristics." How do you determine whether or not something is unique? You have to have been around the proverbial block, you have to have seen a good portion of what is out there to be seen. In other words, you have to have learned what has gone before. If someone learns the mechanical basics of photography and nothing else, and then goes out, shoots a lot, and develops their personal style, it isn't necessarily a unique style. They could find out down the road that all of their shots look like Diane Arbus ripoffs, even if the person had never heard of Diane Arbus.
Developing a unique vision is not something that happens overnight, and it does not happen in a vacuum. It requires years of practice. It requires careful study of technique and good design. It requires critique. It requires careful study of the works of lots of other artists that have come before, as well as careful study of the works of your contemporaries. It requires taking a bit here, a bit there, selectively ignoring that bit over there, and mixing them all up until what comes out on the paper is a true or mostly true reflection of what you see and want to see in your eye, mind, and heart.
All of that requires tutelage, either formally or informally. I have been shooting off and on for 20 years now, and my 'personal, unique vision' is still developing, still changing. The driving force behind that change comes from learning more and more, and being taught more and more.