This paper attempts to present a critique of the concept and meaning of the term social accountability at university level from a critical point of view. The main objective is to analyze and re-build the term accountability in order to contextualize it for public universities. First, we present the importance of the idea of accountability in universities as a way of being and acting. Then, a comprehensive literature review is presented referring to the term University Social Responsibility (USR, hereafter) using the economic thinking of Milton Friedman and Edward Freeman. Subsequently, we look at the meaning of USR within the framework of higher education. Finally, we conclude that it is necessary to rethink the idea of university accountability as opposed to the current policy of USR affecting the policies implemented for public universities.