Well, regarding Stephen King, I've read his excellent book "On Writing" and he actually says that most people will never be 'genius' writers, because the potential to be one is handed out to few people, but a poor writer can become an OK writer and a good writer can become a very good writer if they spend the time learning the craft. I agree with him.
I've said before that I think writing (and comedy) is part "art" - having the flair or divine inspiration if you will, and part "craft" - working and re-working ideas until they sit right. Inspiration and perspiration and all that bollocks.
Not to say that it all comes 'easy' to the gifted few. Think of Eric Morecambe and how painstakingly he went over routines. Clearly a bloody comic genius, but so much work went into it.
I do think Perry's right about needing some foundation of natural talent to build on and all that.