" There is a non-trivial amount of money coming in from other countries to bid up property as well."That is true and one of my neighbors was a realtor for 20 years and has a number of friends who advertise in foreign countries that they can find you an investment property in California. Typically though, those buyers seem to be "status invested" rather than simply buying a house. So they look for places in San Francisco, or Palo Alto, or Saratoga (places where there is some status associated with owning a home there) rather than say Sunnyvale or Santa Clara.
That said, my neighbor came to the US on an H1B with his wife and daughter, is working for a local tech company, and his parents gave him the money for a 20% down payment on his house. That saved him the more typical path it seems of getting a starter house, building a bit of equity and then trading up to a larger house. I expect that being foreign nationals they don't have the gift tax burden that US parents do.
On the one hand that is foreign capital fueling higher house prices but at the same time my wife and I got a loan from her parents to help buy our original house, so I don't consider it out of the ordinary if the parents can help out.