Frankly, I don't see how contradicting someone when they tell you where they are from, and demanding a "real" answer, could be seen as anything other than extremely rude. Like, accusing people of lying at all is rude, let alone about something as conversationally trivial but personally important as one's place of birth.
If there weren't a racial element, the conversation would be baffling. "Where are you from?" "Chicago" "No where are you REALLY from" is a conversation only ever had between a white person and a non-white, because it would not make sense to randomly accuse someone of lying about their place of origin unless you're a racist trying to make someone feel out of place.