Entrusting GenerativeAI (GenAI) to complete tasks that require critical engagement with content can have wide-spread implications to the integrity of student learning outcomes. This paper presents the preliminary findings of a mixed-methods survey of Australian university students (n=399) on their use of GenAI in their studies. Preliminary findings suggest student GenAI use in universities is common, with approximately one third of students using GenAI and 53% engaging with ChatGPT alone. In open-ended responses, stigma and judgement towards students utilising GenAI to complete their assignments is evident. Stigma may entrench a culture of secrecy around integrating GenAI into the student workflow, which may work against any initiatives to increase citation or transparency in the sanctioned use of GenAI. Students also discussed implications for employability, skill development, and the originality of their work, with 80% of students concerned that GenAI is devaluing their degrees. These findings require universities to critically engage with either: building a culture of engagement with, or increasing surveillance against the use of GenAI in student assessments (reflecting the GenAI stance of each university).