You seem to be assuming that the Bay Area has experienced the greatest increase in rents. Looking at the actual numbers is more useful.
Recently, Seattle has experienced the greatest percentage increase in rents[1]. San Francisco and San Jose were up there, but the recent percentage increases in the Bay Area have, for instance, been on par with the increases seen in 2012-2013 in cities like Houston, Miami, San Diego and Boston[2].
It's a tough market out there for lots of people and while it's convenient to think that the Bay Area is always special because of the tech industry, this simply isn't the case.
[1] http://online.wsj.com/news/articles/SB1000142405270230488710...
[2] http://realestate.msn.com/massive-rent-increases-to-continue