First, of course, I have to pause to sigh at the imposed false dilemma. Why is it that humans have such an urge to force ourselves and others to choose "one or the other" when there is no real need to do so? There is absolutely no reason to make one aspect of storytelling more important or more of a focus than another, unless that is your personal preference.I know both the story and the way it's written is important, but if you had to pick one above the other, which would it be and why?
Second, one has to ask what the questioner means by "story" and "the way it's written". This is the missing element that bothers me in so many debates. Terms are seldom defined even though we all tend to mean different things by what we say. To be on the same page in any discussion it is important to understand how we are using certain words, to agree on how to define the terms being discussed. For instance, to me "story" includes the whole package. Story includes the individual elements of the particular story being told (plot, characters, setting, theme, etc.) as well as how it is told by the author (exposition, dramatization, characterization, description, foreshadowing, etc.). So in my opinion there is no such thing as "story" vs. "the way it's written".
However, if you define "the way it's written" as "the technical aspects of writing" such as sentence structure, word choice, and techniques based in the words themselves such as alliteration then I think there is a very important difference between "storytelling" and "writing". A difference that one has to think back to the oral storytellers of other eras to fully appreciate.
Now I agree with him to an extent. These are real problems with the written down, read story. However, I disagree that these are unchangeable qualities of the read story. I don't think it has to be that way. I think authors have been taught to write that way. Yet I have read many stories in books where the author's voice came through so well that I did feel I was being told a story and it felt alive. I love those stories more than any others. Yet across the internet I see the advice to stay far away from the feeling of the "told story", to keep yourself separate from the story. I think this is terrible advice. I think it is a real detriment to literature. In addition, the advice I see across the internet focuses on technical aspects of writing. We are told to improve our storytelling by avoiding certain types of words to avoid any storytelling technique that presents even the slightest challenge. Our tools are removed from our hands by the so called experts and we are patted on the head and told to be a good little author and write things that appeal to critics (agents and editors) instead of readers.
We have certainly all but lost the art of good storytelling, which, as Seumas MacManus says, "was ever a propagator of joy". I think that in losing the art we've also lost the joy. My goal, at least, is to try to find it again and do what I can to propagate it a little. That's what's important to me as a reader and a writer.