We conducted a within-subject experiment involving 13 participants that empirically explore how two different models of story delivery involving information visualization influence audience-constructed narratives. The first model involves a speaker using visualization software to communicate a direct narrative, while the second involves constructing a story by interactively exploring visualization software. We used an open-ended questionnaire in controlled laboratory settings, with the primary goal of collecting a number of stories derived from the two models, followed by two Likert-scale questions on the ease of telling and curiosity about the story in each delivery model. We qualitatively analysed the stories constructed by the participants, based on a number of themes tied to storytelling, including time and place and narrative structure. The study's results reveal some interesting possible differences in how users receive, interpret, and create stories in each case.