True, but did they grow up here?
YES.
I can't tell you how many times I've corrected born and raised Fort Worthians on that...
How dare they? Seriously, who do these people think they are? We can't have people misusing the label "downtown" with respect to a retail development that sits at least a half mile outside of it. If we let these hooligans go unchecked, the next step is complete anarchy!
I think it comes from the suburban sprawl mindset. People who live and spend most of their time outside of Loop 820 just aren't as familiar with the neighborhoods in the city core. A lot of them see Fairmount (or at least Magnolia) as part of downtown as well.
A guy I used to work with is one of those people: When he relocated to Ft Worth, he stayed at the Residence Inn in the Cultural District (W7). He considered that "downtown." Close, but not quite.
It's easy to be kind of pedantic about it, since most of downtown has strict boundaries: The Trinity River, I-30/Lancaster corridor, the train tracks to the east. Those boundaries contain Downtown and the Upper Westside. If you're outside of that, you're not Downtown.