Chuck Klosterman is believable, or credible, as a writer because of his honesty. He is very transparent in his writing; he gives his opinion about anything and everything, no matter how brutal or frank. Even though his pieces are notoriously slanted, Klosterman presents his opinions in a way that helps his readers to understand him as a writer.
Klosterman's voice is another thing that effectively portrays his attention to detail. Throughout the article, Klosterman posts links that lead to resources about the subject matter of the article. He makes it easy for the reader to understand exactly what he is talking about for the entire article. Without these links, we would have to take Klosterman's word for it. With the links, we are able to experience it for ourselves.
Overall, Klosterman's writing appears credible simply because he writes intelligently. His writing makes him sound intelligent, and that makes people trust him to a certain extent.