I'm talking about San Francisco, not the 5,500+ square miles of faceless suburbs surrounding the city.

Sao Paulo (city proper): http://en.wikipedia.org/wiki/S%C3%A3o_Paulo (18,690/sq mi).

San Francisco (city proper): http://en.wikipedia.org/wiki/San_Francisco (17,620/sq mi).

The metro area density is mostly a measure of whether the suburbs are more or less urbanized. E.g. the LA/OC metro CSA is substantially more dense than the SF/Oakland/Fremont CSA, but nobody would say that LA is denser than SF. Rather, LA is surrounded by urban sprawl while SF is surrounded by suburbs.