The concept of the "public university" has been widely promoted as the principal alternative vision for higher education to the neoliberal, managerialist model that currently prevails. However, if the public university is to serve as the holder for collective ideals of a just, sustainable and democratic future in higher education, then there is a need to think through carefully what this concept actually means in practice, in order that it does not become an empty, misleading form of public relations rhetoric. This article uses the example of assessment to argue that if the public university is to perform the role of fostering critical, reflexive, independent and democratically minded thinkers -- a role that has been universally embraced by its promoters -- then the use of grading in higher education assessment needs to be strongly contested.