There are 7 million people who live in the greater Bay area and they live in ~2.5M owner-occupied housing units. I can't see tech millionaires making that much of a an impact on housing prices. Sure, they could push prices up by 10-20%, but SF housing prices have pretty much doubled since the great recession.
I think it's the "now or never" mentality of home buyers. they think that prices will only ever go up, so if they don't buy now (even if it means overextending themselves) they'll never have a home. I'm sure a lot of people thought the same thing before the housing crash of 2007.