Wrong. Very very incredibly wrong. Substantially more than half of all incidents of cancer are the result of random mutation. No amount of "eating right" will change that.
Careful, a little knowledge is a dangerous thing.
(Almost) all cancers are the result of random mutation (there's a few infectious cancers in dogs and Tasmanian devils which aren't). And eating right can decrease the rate of random mutation, directly (antioxidants) or indirectly (general health, note also that stress increases mutation rate). Most likely the main benefits of eating right are metabolic syndrome and cardiovascular disease and general health, but those are themselves very good reasons.
Like with smoking, there are certain things you can eat which will increase your rate of mutation. Not eating those means you're less likely to get cancer than those who do. Agreed with you about the "organic foods" farce; those are sometimes better and sometimes worse, and worse is usually cheaper.