It might all come down to:
My take is that if the doctor and his office are not directly part of the actual school (ie. teaching, research, etc) and its primary educational activities (or necessary support) then it would not be covered as "educational property".§ 14-269.2. Weapons on campus or other educational property.(a) The following definitions apply to this section: (1) Educational property. - Any school building or bus, school campus, grounds, recreational area, athletic field, or other property owned, used, or operated by any board of education or school board of trustees, or directors for the administration of any school.
Otherwise, if the university owned a strip shopping center it would be illegal to carry there.