Narrative psychology is probably the go-to domain of research and theory for questions about the power and popularity of stories. Here's an excerpt from the Wikipedia page (with added emphasis):
Narrative psychology is...concerned with the "storied nature of human conduct" [(Sarbin, 1986)] or...how human[s]...deal with experience by constructing stories and listening to the stories of others. Operating under the assumption that human activity and experience are filled with "meaning" and stories, rather than logical arguments or lawful formulations...[this] dichotomy...[appears (Bruner, 1990)] as a distinction between "paradigmatic" and "narrative" forms of thought, in his understanding they are both fundamental but irreducible one to the another.
According to Sarbin (1986) "narrative" is a root metaphor for psychology that should replace the mechanistic and organic metaphors which shaped so much theory and research in the discipline over the past century. The indisputable physical events of a personal occurrence are different from a story that results from the storied cause and effect relationships. (McKinnon) [citation unavailable]
...Independent of any fiction in the actual physical matter told, are physical events that are as unequivocal as quantum mechanics and human chemistry.
I'm unfamiliar with examples of narrative psychological research of the sort you're looking for specifically, but the above seems to argue from psychological theory at least that narratives gain appeal and influence from their apparent factuality. Narratives may not claim to apply their principles generally, let alone acknowledge any limits to their generality, but maybe people naturally infer generality anyway, and are less likely to recognize limits on their own when they aren't mentioned...This is just speculation though.
One other idea that's at least equally worth mentioning (which may not be saying much) is that narratives are particularly influential in the study of identity. Tying negative events in one's life into a redemptive life narrative relates to well-being, though causality isn't clear in this relationship (McAdams & McLean, 2013). Maybe a similar principle applies from an observer's perspective: maybe consumers of stories "create meaning" vicariously by putting both good and bad events in the shared context of others' lives. Maybe advertisers' messages are more subtly appealing (and less overbearing) when embedded in the narratives of relatable, likable characters that seem to have more to say than just what their favorite shampoo is. Again, this is speculation; I'm no advertiser. I mostly hope I've given you some ideas to follow up on in study of the areas of psychological research with which I am somewhat familiar: narrative identity, and narrative psychology in general.
Bruner, J. S. (1990). Acts of meaning. Harvard University Press.
McAdams, D. P., & McLean, K. C. (2013). Narrative identity. Current Directions in Psychological Science, 22(3), 233–238.
Sarbin, T. R. (1986). Narrative psychology: The storied nature of human conduct. Praeger Publishers / Greenwood Publishing Group.