I agree, and would extend what you wrote about a ceiling on talent to kinds of talent. I think what kind of talents you have play into whether people think your writing is great or whether you're a good technician or a good storyteller.
For example, lateral thinking versus empathy. You can be extremely smart and not be good at lateral thinking. If you lack lateral thinking, it limits what you can do with your plot. Twists, turns and solutions that make some stories great just won't occur to you. If you lack empathy, or just don't have a lot of insight into people's psychology, it'll limit what your characters are like.
I may be projecting here, because I know from my work life that I'm good at lateral thinking, but I know from my reading life that I lack an appreciation for subtle psychological stuff like you see in, for example, the great Russian writers. I bought a book in which a professor broke down what made some famous Russian short stories great. I got it, but only after he explained what they were doing. Now I can see that kind of subtlety better, but I don't read for that kind of thing, so I don't think I'll ever write that kind of thing, either. So, if your definition of a "great" writer is somebody who turns out stories full of subtle psychological impact, I'll never be a great writer no matter how good I get at turning a phrase. If your definition of a great writer is somebody who can tell a really entertaining story well, I might be able to get there.
In this case, I think King was probably thinking of "great" like Dostoevsky or Shakespeare, writers who could portray the deepest parts of the human experience and make them relatable to readers. Few writers could ever get there, no matter how hard they tried. And for my part, thank goodness.
I am just about done with <em>A Swim in a Pond in the Rain,</em> by (one of my favorite short story authors) George Saunders. It's an awesome format: it is 7 short stories by famous Russian authors (Chekhov, Tolstoy, Gogol, and Turgenev), each followed by an essay analyzing the story/what makes it great, and connecting it to broader lessons about the storytelling/writing process. It also includes a good deal about Saunders' own process.
I had no particular interest in Russian short stories going into it, but I thoroughly enjoyed it! If you are into audiobooks, the audio version is fantastic. Saunders reads the essay parts himself (he's got a great voice), and they have a different narrator for each story.