Employing a statistical modeling inspired pedagogy is becoming a widespread practice in the statistics education community. Many have incorporated the practice of formulating conjectures in their modeling-enhanced educational designs and have reported on its benefits. We further elucidate the mechanism through which students' conjecturing may be beneficial, in particular to their emergent reasoning with informal statistical models and modeling, as well as examine what challenges it may entail -- the double-edged sword of conjecturing. We introduce a framework to describe young learners' reasoning with informal statistical models and modeling (RISM), in which students' conjecturing is represented as one of two parallel planes of model creation and refinement. We offer a case study of a pair of students' participation in an integrated modeling learning sequence, including both real-world modeling tasks and probability-world modeling tasks. The pair was chosen as both students held strong, opposing real-world conjectures. Our goal is to elucidate the roles these conjectures can play, for better or for worse, to fully harvest the pedagogical potential of conjecturing.