That's not the parent's point. If I buy a $1M home in CA 10 years ago and I pay 1% in taxes then and the house is worth $2M 10 years later, I don't get charged 1% of $2M after 10 years. I get charged a marginal increase ever year and this increase isn't based on market norms (I forget what the actual # is, but it would be like paying 1% of $1.25M). This means, if I sell my $2M house after 10 years), and buy another $2M house next door, my taxes are way higher in my second home due to prop 13.

Depending on your age, you may be able to not get dinged with the new home's taxed value.[1]

[1] http://www.boe.ca.gov/proptaxes/faqs/propositions60_90.htm