Subsidized corn has a massive effect on decreasing food prices. People may not need high fructose corn syrup, but they need food and a lot of food has corn syrup in it. Cheaper feed leads to cheaper meat. Cheaper ethanol leads to cheaper fuel which makes everything a little less expensive.

I can't vouch for corn subsidies being the best way to lower prices, but it's certainly a powerful lever that decreases food prices across the board.