Krugman shows that according to a paper on the Chicago Fed, there is no evidence of a connection between core inflation (without energy and food prices) and commodity prices. He should have said no evidence in the United States. In fact, when you look at developing countries the connection might be stronger. That depends on the pass-through effect from commodity (tradables) prices to non-tradables.
Also, note that the Consumer Price Index (CPI) would be affected. For example, if we look (see graph above) at the Argentine data (using terms of trade and consumer prices) there is a clear effect of commodity prices on CPI inflation. That does not mean that I would favor hiking rates of interest, and putting a break, in the US or Argentina for that matter, on expansionist policies. Quite the opposite, the suggestion is that policies to stabilize the wild fluctuation of commodity prices, for starters try to control the speculation with commodity derivatives, might be a good idea.