This is, to put it charitably, a misconception.
Leaving aside the fact that most RPGs are unafraid to use the word story in describing what the game is about, statements about the disconnect between "story" and "roleplaying game" are more often tools put to political use within the culture of gaming than they are accurate descriptions of gaming. The core idea explicit in such statements is used to justify an artificial boundary between "real roleplaying games" and "storygames," or as a defense of supposedly "pure" styles of play.
All sorts of faulty arguments are made to uphold those beliefs. "Roleplaying games have narratives, not stories," claim those who don't understand that in common usage "story" and "narrative" are synonymous. "If there is a story it can't be a game because stories are carefully plotted things with endings decided long before the page gets written," say those who have never met a actual author who could tell them, from experience, otherwise. "RPGs are about immersion in a role, not stories!" cry those who have not yet made the connection that generally when you take on a fictional role you do so within story.
Feet are held to the fire when you really think about what it is that you do when you play a roleplaying game. If you are playing a character in a roleplaying game, you portray their actions, make their decisions, and sharpen their perspective on the fictional world through which they move based on the results of their past actions, the outcomes of their previous decisions, and what they have come to know about the setting that surrounds and defines them. All of the choices you make while in the role of that character are choices based on what has already happened in that character's story.
The truth is that this is part of human nature, as far as we understand it: we process our lives as an ongoing narrative, a story in which we are the protagonist. If someone were to ask you, "Hey, what's your story, pal?" you would be able to answer them based on the things that have happened to you, your upbringing, the events you've taken part in, the other people you're connected to, etc. If someone asked you, "What did you do yesterday," you would relate the previous day's events in narrative form. You have a story, you are in an ongoing story, and it is a story you can relate without the story having concluded.
If an roleplaying game stopped and you explained the events of the game to an interested non-participant, you probably wouldn't hesitate to call the verbal act you're engaging in a story. And yet, the same events you could describe are no less a story when they are in motion. While you are playing the game, you are treating those events as a story, as a narrative that has happened in the past and bears weight in the here and now; those events are the previous chapters and preceding lines of the story in progress, and if you are roleplaying a character you behave as if the story is there because you are using it as the raw material through which you capture a faithful likeness of who that character is, why they do the things they do, and what shapes their personality.
Some may argue that this does not truly count as a story because it is not fixed in its outcome and because it is being created on-the-fly. In this sense, roleplaying games are like improvisation, and successful improvisation depends upon remembering what has happened before in the story currently generated by unscripted acting; as Keith Johnstone states, "The improviser has to be like a man walking backwards. He sees where he has been, but he pays no attention to the future. His story can take him anywhere, but he must still 'balance' it, and give it shape, by remembering incidents that have been shelved and reincorporating them" (Impro: Improvisation and the Theatre 116).
The notion of creating the fictional present in acting--what Johnstone rightfully calls the "story" of the improvised character--is full predicated on "incidents" of the past. In improvisation and in roleplaying, the story is happening right in front of you: it is a series of events you are reacting to, building on, interrogating, and bouncing off of. It is not "finished," it is under construction, but it is present for all intents and purposes. And to play a roleplaying game, you accept that it is present, even if you're not comfortable with naming it as a story.
