CPI, as the name suggests, is based on consumer prices. They're not taking the price of wheat features and calling it a day.
Of course I agree with you about how CPI samples are taken and that they are representative of the market as a whole.
tl;dr: I agree with you, I'm just floating a theory as to why some people may have significantly different experiences on a micro level.
This is what I’m seeing, anecdotally. In towns with more than one non-affiliated grocer, prices are cheap. In towns with consolidated groceries, prices are higher. Enough that the “savvy” shoppers, i.e. those with a car and time and liquidity to enable bulk buying, drive to the next town over.
(a) Kroger - Kroger, Ralphs, Dillons, Smith’s, King Soopers, Fry’s, QFC, City Market, Owen’s, Jay C, Pay Less, Baker’s, Gerbes, Harris Teeter, Pick ‘n Save, Metro Market, Mariano’s, Fred Meyer, Dillons Marketplace, Fry’s Marketplace, King Soopers Marketplace, Kroger Marketplace, Smith’s Marketplace, Food 4 Less, Foods Co.
(b) Cerberus Capital Management - Albertons, Acme Markets, Carrs-Safeway, Haggen, Jewel-Osco, Kings, Pavilions, Plated, Randalls, Safeway, Shaw's and Star Market, Tom Thumb, United Supermarkets, Vons.
While those core goods prices are I believe accurate, the prices at point of sale have gone up significantly more - especially in places that went from having a competitive grocery market to, well not.
Note that restaurants have done a significantly better job of controlling ingredient costs specifically because they don't shop at grocery chains.