That is exactly right. I knew about this. Most of the homes I have looked at, while they have lost a lot of value, were still in the money for the previous owner so my purchase price would have been above the last one and I would pay taxes on my price.

Those few that were less indeed I just pick up the old tax until I can ask for reassement during the window.

Prop 13 was passed to protect folks from huge jumps in values greatly increasing their property taxes and did not contemplate reductions. So while it provided for fixed modest incremental increases every year to assessed values, it never provided for fixed reductions if market values dropped. It was later that the legislature passed a law that allowed you to request a reassessment if market values dropped. That reassessment, by the way, is not permanent and resets after a while.