Of course writing can be taught. Great technical writing is not what makes authors great. When an author has been deemed great it is because of the content of the story, the flesh of his world, and the depth of his character. Great technical writing doesn't contribute to this, it just makes it easier on the reader to read the meat of the book. Writing technique is like a smooth road versus a bumpy road. Both can have a great destination, but the smooth road allows for the driver to not be distracted by pot holes and unlit lanes.
The greatness that, I think, people are said to be born with is their imagination foresight. I have never heard of someone honing their imagination skill.
I hope one day I can be a genius... Considering the time it takes to become one, I should have started a few years ago.