The real world tends to generate "history", not "story". Note the relation of the words.
Context matters here. I can accept your position under the stipulation that there're some gaming styles that are more focused on exploration of a fictional world and those will indeed inly generate history, not story. But I think that those styles are far less common than the ones that are based on exploration of a story. Note the difference between the setting being the game in contrast to the story being the game and the setting only being the background and facilitator to it.