Supervision in higher education (HE) often balances the tension between fostering student autonomy and providing sufficient guidance, especially within undergraduate programs. This paper explores an under-researched area: the dynamics of group supervision in undergraduate education, specifically how students challenge their supervisor's expertise. Using video recordings of a group of engineering students at Aalborg University working within a Problem-Based Learning (PBL) framework, the study investigates moments of disagreement between students and their supervisor during project supervision. Employing conversation analysis (CA), the study examines the negotiation of epistemic claims--where students draw on their experience to challenge the supervisor's expertise--and the subsequent impact on the learning trajectories. The findings highlight that students use their epistemic authority from experience to challenge their supervisor's proposed academic direction, while the supervisor defends their stance based on disciplinary knowledge. The study emphasizes the importance of aligning cognitive congruence and situated learning to facilitate productive supervision interactions. Ultimately, the paper sheds light on the critical yet often overlooked role of student agency in supervision and offers insights into improving the supervisory process in HE, particularly in group settings.