My understanding of property tax in SF is that it is based on the price the house was purchased at. This means that the home you've owned forever has had a predictable tax based on that price, and only new owners you sell it to will be paying the higher cost tied to higher property value.
Really, the article left out that HUGE issue. If you grew up in the Bay, you are very very familiar with this. I am surprised how many commenters here claim to live in the Bay, yet don't understand property taxes in California. It's a major issue in the state, not quite as big as water rights, but still major.