No, in fact, I think it is more accurate than just going by "city-proper". I don't think of Pittsburgh as one city with 300,000 people, I think of it as an area with 2.5 million.
Despite the fact that the outer fringes of the area are absolutely nothing like inner Pittsburgh?
If city limits were divided like that then Bronx, Brooklyn, Queens, Manhattan, etc. would all be different cities. Different interests, building styles, and industries shouldn't mean it's not all one city. If anything, it makes it MORE urban.
If you don't want people to think you live in a suburb, refer to your location as "Downtown Minneapolis" or something so people get a vision of skyscrapers in their head.