It's clearly not "completely" disconnected, otherwise there would be zero volatility in supermarket prices. But again a price is a price not matter what layer of the market it sits at, and all prices are subject to market conditions. Freaking out about some subsampling of them as being "real" in/de/stag/whateverflation in an attempt to shoehorn whatever noisy data you have into a signal that confirms your priors just leads to the kind of nonsense logic that produced the analysis I quoted above.