Right. The actual boundaries of a city are often the result of historical accident and depend on the governmental power structure of the region. "White flight" and "urban decay" cause people to live as close to a city as possible without actually living within it. I think the inclusive meaning is even truer in areas of greater sprawl, e.g. most of US and Asia. Los Angeles is a big city, but when people talk about LA they often mean the entire county or more.