The annual cost-of-living adjustment in Social Security payments are not based on the core rate, but rather on CPI-W (one of the sub-indexes of the CPI). Details are here (on the Social Security Administration's web site):

http://www.ssa.gov/OACT/COLA/colasummary.html

I'm totally with you on the CPI understating actual inflation (as anyone who keeps track of their household expenses from year to year can verify). The details vary enormously from household to household, of course. (My renters insurance didn't go up nearly as much as your homeowner's insurance, for example, plus it's a much smaller portion of my annual budget.)

I'm actually planning another article on the CPI, that will talk about "hedonic adjustments"--how the CPI is adjusted to try to account for the fact that some goods (such as computers) have about the same price from one year to the next, but are actually better. It's not a crazy idea, but I think it's done in a way that cause the CPI to understate inflation.

This post, though, was just about the core rate. That's a useful value for making policy decisions. I don't think anyone uses it to adjust cost of living for anything.