San Francisco[0] proper has a higher density than London[1], and slightly lower density than Paris[2] — two cities that have thriving subway + commuter rail systems.
I think you mixed up imperial and metric systems --- San Francisco has 18,451 people/sq mi. Paris has 55,000 people/sq mi. It's almost three times as much.
There's got to be a more useful metric than average city density; the 2010 US Census [0] places the 5 densest cities in the US as having a population under 70,000 (yes, I'm quoting Wikipedia). City planners must have a unit more like person-acres or something to get an idea of the actual spread of the density.
Standard density quotes for cities can be pretty misleading as it often reflects fairly arbitrary divisions. For example while Paris is indeed reasonably dense the oft quoted number is for a fairly small parcel of central Paris.