Actually I do recall meeting some people in one "tourist's destination" place who answered "we're from San Francisco" to "where are you guys from?" and then later specified they from bay area not far from SF (I myself live in SF). It's a matter of convenience I guess, when you are in the place with plenty of people from different regions it will quickly give an idea what part of US you're from without going into detailed explanations when not necessary.
When people ask me where I'm from I say "DC". I actually grew up in Alexandria, VA. But I'm not lying to those people[1], I'm trying to give them a general idea of where I'm from that they are most likely to know. If they follow up with "what part of DC" then I know they are more familiar with the area and I say something like "well actually, i grew up outside DC in northern virginia".
Now that I live in Oakland I say I live in Oakland, but if I lived in, say, fremont, I'd probably just say the SF Bay Area. People probably know Berkeley, Oakland, SF, Palo Alto, and San Jose as specific places around the bay, so you can safely say those, but if you are from Walnut Creek...no one (generally) outside of the area can actually place that, so defaulting to "SF Bay Area" or even "SF" is simpler and puts the person you are talking to in the right geographical area.
