Sam has the privileged position of being president of the student body.
Does the above mean that because of being president of the student body, Sam enjoys some privilege? Thanks.
It might do, depending on the body concerned.
However, it is a standard collocation indicating that the person has a particular position in the community, which allows him certain rights. For instance, the president of the student body will be the spokesman for that body, and will possibly be able to appoint officers within the student body [Treasurer/Secretary etc.].