I can confirm that I have this problem with Lexington, KY as well (example). Roads with the same name in nearby towns, roads that go on for miles out of city limits, etc.
I assume my particular case would be easy to solve since Lexington is a consolidated county-city government and has a simple border. However, since we don’t have the “blue line”, I guess that OpenStreetMaps doesn’t have an administrative border added for my city. I looked up how to add one, and I came across a forum post where @JamesChevalier was asking about it and was basically discouraged from doing it because of its difficulty.