This study investigated students' perceptions towards translanguaging in their English-medium instruction (EMI) experiences to understand how it affects their access to the subject content. The focus is on EMI at a leading, research-intensive university in South Korea, qualitatively explored using data collected from interviews with ten undergraduate students, and analysed using the principles of constructivist grounded theory. The emerging theory indicates that students' experiences of 'monolingually framed' shifts between L1 and L2 systems can be understood using the notion of 'trust' and that trust reinforces binary choices, in particular EMI situations, of using either the L1 or the L2 system. Further discussion indicates that, over time, these patterns of trust may constrain learning. The study suggests that instilling a competence of translanguaging in students will help them overcome these constraints. Pedagogic implications are discussed for ELT practitioners who prepare students for EMI and/or support EMI content instructors in their teaching practices.