Who decides a university's stance on a topic?
Universities work like any organization. The stance of the organization is the stance of its leadership. It can be the president, the chancellor, whatever you call it, it can be the board of directors, it can be the faculty assembly… It can even be a university-wide poll as you suggest. It depends on how the university is governed.

The statement "organization X has position Y" is a very common one in English. For example, "country X is a friend of country Y". "Statistically", it's unlikely that every single inhabitant of country X is actually a friend of every single inhabitant of country Y. Saying that a group of people does something is not the same as saying that every single member of that group does something.