As to the location, many state-sponsored colleges across the country have mulitple locations. And stickers like “University of *State *- Location” are very common. Students & former students have allegience to their campus, not to the overall state U system.
As to the major, did the car the OP saw really indicate the owner’s major, or the owner’s school within the campus? Big difference. Some campuses have both well-respected and much-derided schools sitting side by side.
Ultimately, every university sticker is either a stealth-brag, or an appeal to group membership. I don’t see the downside in somebody choosing any particular layer of membership vs. another.
How does it really differ if somebody says
I graduated college.
I graduated from some State U.
I graduated from some state U in PA.
I graduated from a particular state U campus in PA.
I graduated from a particular school in a particular state U campus in PA.
I graduated with a particular major from a particular school in a particular state U campus in PA.
Hint: To those of us not from PA, we’re not sure any of those actually mean you can read. 
