Americans would disagree! See:

http://www4.uwm.edu/FLL/linguistics/dialect/staticmaps/q_95....

Also, perhaps even moreso than other places in the US, "The City" (capitalized, with extra stress on each syllable) has long been an affectation in the Bay Area & Northern California to refer to San Francisco proper. See especially the columns of Herb Caen and regional anthems like Journey's "When The Lights Go Down (in The City)".

You must not be from the Bay Area. San Francisco is "The City", "San Francisco", or "SF" to anyone who lives or has ever lived in the Bay Area.

Sorry, "The City" is a local reference term. Just like "The Store". Trying to dereference without a local frame leads to confusion.

As someone who is only familiar with calling San Francisco "The City", I am curious what city outside of North America you are referring to; please enlighten us.