Should make sense. Here's some BLS CPI data:
Any influence total inflation seems to have on core inflation seems small at best. Admittedly, this includes food prices as well, but energy prices have been jumping over the past several years, and the chart, to some extent, should account for that.
And Mark Thoma on why we use Core Inflation:
.... this paper finds that predictions of future inflation based upon core measures are more accurate than predictions based upon total inflation.
Hat-tip to Economist's View.