Yes, you pay an SF premium. You pay a premium for most major cities, and the worse housing is, the higher the premium. But I'd bet moving to the South Bay isn't happening for that reason. SF pricing has a halo effect on the South Bay, and your savings will be minimal, if any. (I see little differences in South Bay and SF salaries, for larger companies)
What I'd wager precipitated the move is SF rents are stupidly high , and then you combine that with half the twitter offices being empty. If you believe loopt, San Jose office space is ~ half the cost of SF. Half the space, at half again cost - their real estate bill shrinks by 75%. And given that Twitters bill is likely ~$40M-50M/month, that's a good chunk of savings.