I grew up in the San Francisco Bay Area and live in San Francisco now and we don't seem to have this problem. At least, (and I could be outta the loop) I've never encountered it. Growing up, I'd tell people I'm from Fremont and if they had no clue what I was talking about, I'd say I live in the SF Bay Area.
These days people are mostly prideful of where they live, so they'll say they live in Oakland or the East Bay, San Jose or the South Bay, etc. I think because it's no more a badge of honor to say you live in San Francisco than to say you live anywhere else in the Bay. Though where you live in the Bay can be (but not always) telling of what type of person you are.
Conversely, when it lived in Phoenix (North Phoenix to be exact) and told people that, they always ask where, assuming I lived in one of the metro area cities/suburbs.
Typing on a giant phone - there will be funky grammar and typos.
Curl Style: 3b/3c
: Giovanni TTTT (my hair loves this)
: GVP CB or DevaCurl One Condition, occasionally with honey
: Biotera Styling Gel, BioSilk RHG
: AG Re:coil, CJ Beauticurls, Lube
Hair hates Aloe Vera & Avocado