That's not so much an issue with grain prices. Rice and bread and such are the most basic of staple foods, and pricing people out of that market results in hunger and starvation.

But huge amounts of the staples the US produces are then fed to animals to make meat. It takes something like ten pounds of grain to make a pound of hamburger. If food gets more expensive people cut back on meat, which frees up more grain.

That is true in the US, but not as true in other countries. The US eats an enormous amount of meat compared to most countries (and even more so compared to history).

The article mentions that it would be better if some of the farmers started growing vegetables rather than grain, but the subsidies don't pay for vegetables.

There are multiple kinds of rice, some area cheaper and easier to grow than others.

Same for wheat - low gluten types are cheaper. (Which is basically why they invented the http://en.wikipedia.org/wiki/Chorleywood_bread_process )