Well plants have about 5-10% of their mass in carcinogens that are naturally occurring. These are at higher or lower levels depending on growing conditions and are part of the self-defenses of the plant. Plants don't have claws or teeth, they defend themselves by making themselves poisonous to bugs or other things that would eat them.
Case in point: A "bug resistant" potato was developed. It was marketed, but several people got sick eating it from too high a solanine content. (google solanine poisoning, kids can die of eating potatoes, even regular ones)
Just because something is "natural" doesn't mean it's benign.
Also I think organic vs non organic is only part of the story. Let me illustrate with an example from my cancer journey with my mom...
Most people are deficient in selenium.
Soils that we grow food in are deficient in selenium, and more so because we keep pouring on the chemical fertilizer, which uses up the minerals faster and faster, so micronutrients like selenium are depleted and have been for along time.
The only way to replace that is to use some kind of mineral replacement like a ground rock or volcanic ash. Literally move rock from someplace else to the depleted area.
This however, is not part of the organic standard. Complete nutritional value of food is not the goal of organic... avoidance of "unnatural" chemicals is.
Although some farmers do focus on complete nutritional value of food they grow, that isn't what the majority care about. Labeling and distribution is more important, a higher priority for most of the big growers.
Moral: local farm markets are a good thing
Moral 2: Chemicals did get us into the mess in the first place, so avoiding them is good... but if you don't solve the problem, or only take minimal steps, well... you only get out what you put in..
On the plus side:
http://www.sciencedaily.com/releases/2012/07/120703120630.htm