It's also pretty common to live outside the city and commute in on Metro (DC's Metro is built more like a commuter rail than a urban subway system).
I think the tricky part is that there really aren't many apartment buildings in DC to begin with, aside from the recently built and very overpriced luxury condo conversions, so the supply of one bedroom apartments is low. If you can stand to have roommates, you're much better off with a 2 bedroom English basement or a 3-4 bedroom little rowhouse.
The rent is higher in SF, but the tradeoff is that you can walk or ride a bike everywhere, year round. It's possible to get by in SF without a car at all. In DC (or elsewhere) you're paying for parking, gas, insurance, and a monthly car payment. That starts to add up pretty quickly. There's not an $11k a year difference without that ($1.4k vs $2.7k isn't realistic), but factoring it in, SF really closes that gap, or likely becomes cheaper.
So what. Market has spoken. His rent is X and your rent is X-market discount for living in DC.