The "story" in agile development's "user story" is not a narrative in the traditional sense of the word. Many are short on verbs, which is a big hint that something non-narrative is going on. "User story" is shorthand for a set of concepts and principles. The danger with taking a simple word like "story" and assigning it a new meaning is that novices, and occasionally even experts, confuse the jargon with the traditional definition.

An example of an expert forgetting the jargon of "user story" is in a small section of Mike Cohn's otherwise great book User Stories Applied. Here, the author is talking about the benefits of user stories over other ways of specifying requirements:

Additionally, a study in the late 1970s found that people are better able to remember events if they are organized into stories (Bower, Black and Turner 1979). Even better, study participants had better recall of both stated actions as well as inferred actions. That is, not only do stories facilitate recall of stated actions, they facilitate recall of the unstated actions. The stories we write can be more terse than traditional requirement specifications or even use cases, and because they are written and discussed as stories, recall will be greater. 

While I haven't read the study mentioned (maybe this is the abstract?) I doubt they were studying agile "user stories" back in 1979. From what I've been able to gather from secondary sources, they were studying how stories (in the narrative sense) have a more abstract representation than the actual words that are said, and that memory relies more on that abstract representation such that it's hard to remember if something was explicitly said in the story or just implied.

In short, applying the results of this study to user stories is pretty bogus.