> in California, Proposition 13 lowered the legal tax rate and also changed the assessed value to be the price that you (or your ancestors thanks to Proposition 58 and 193) originally acquired the property, adjusted for inflation.

No, it didn't.

It's the lower of the actual fair market value or the value at time of qualifying event (mostly purchase and other non-exempt transfer, but certain improvements also are included at their full value) plus 2%/year. The actual rate of inflation is not a factor.