I think all authors can be considered reliable. They may sometimes use a narrator who is or is not reliable. But in "Hills Like White Elephants," Hemingway is not using a fictitious narrator; he is writing in what is called third-person omniscient. Whatever he says is reliable, although he may have left out a great deal of information, as he liked to do in his short stories. There is a big difference between a reliable author and a reliable narrator.

Ernest Hemingway, in “Hills Like White Elephants,” tells the story mainly through two devices, dialogue, and an impersonal narrative voice. Because the characters, in a sense, tell their own stories, one gets an almost impersonally journalistic sense of the narrator. Since the narration occupies only seven paragraphs and is primarily descriptive, one gets a sense that the narrator is “reliable” in a traditional sense. On the other hand, the story is fiction, constructed by an author with some strong personal issues about male-female relationships, and the dialogue is not “real” reported dialogue, but rather an imagined conversation that the author manipulates to create certain audience responses, and thus not a reliable guide to how real relationships function.