Who decides a university's stance on a topic? To illustrate what I'm thinking of, this page by UCL on Brexit says:

Are EU students welcome in London?
Yes. In the words of Sadiq Khan, Mayor of London: &quot;To the almost one million Europeans living in London ... you are welcome here.&quot; UCL fully endorses this statement.

There are tens of thousands of staff and students at the university, so it's statistically unlikely that they all endorse the statement. Who, then, decides that UCL indeed fully endorses this statement? He or she is speaking for the entire university. Does he/she know if indeed the majority of staff and students at UCL endorse the statement? If so, how?
If I had to guess, I'd hazard that the Vice Chancellor decides for the university as a whole, but I don't know if it is a solo decision, if the Vice Chancellor conducted a poll of the permanent staff (presumably not the students), or if the Vice Chancellor simply assumed that the university needs EU students for revenue so they had better endorse the statement.
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.