Tyler Cowen argues in a TED talk (~15 min) that stories pervade our mental lives. He thinks they are a major source of cognitive biases and, on the margin, we should be more suspicious of them - especially simple stories. Here's an interesting quote about the meta-level:
What story do you take away from Tyler Cowen? ...Another possibility is you might tell a story of rebirth. You might say, "I used to think too much in terms of stories, but then I heard Tyler Cowen, and now I think less in terms of stories". ...You could also tell a story of deep tragedy. "This guy Tyler Cowen came and he told us not to think in terms of stories, but all he could do was tell us stories about how other people think too much in terms of stories."
You can't not think in terms of stories, that is simply how our minds work. All you can do is to try to keep that (in the form of "intuition") from preventing the adequate weighing of statistics, probabilities, and explicit evidence that can't easily be fit into narratives.
Added: Even when thinking with images or kinesthetically, a person can only use the images or feelings as isolated "facts" or as part of a consistent sequence which has all the same problems as verbal stories.