Universal Design has been promoted to address the diversity of learners in higher education. However, rarely have Universal Design implementations been evaluated by listening to the voices of disabled students. For this study, we investigated the perceptions of three disabled students who took part in an undergraduate mathematics course designed with the principles of Universal Design for Learning and Assessment. The study consists of two parts. First, we observed the experiences students had in relation to the accessibility of the course design. The second part consisted of a further analysis of the students identifying processes to understand how they talked about their learning disabilities during the course. Our results highlight many opportunities and challenges that the course offered to the students, whilst also raising concerns about how the students excluded themselves from their student cohort in their identifying narratives. Based on our results, we argue that Universal Design should be returned to its roots by connecting it with the social model of disability. We call for future research to learn from our mistakes and consider the identifying processes of the students while designing, and hopefully co-designing, inclusive learning environments in mathematics.