Could you do it through foods alone? Yes, I think so under ideal conditions and home grown.
Simple is best and I would try to do it whole foods, nuts and oils such as fruit, seed and nut oils.
ALL of my research points to the body being able to produce EVERYTHING it needs given the right water\oil\mineral balance with the exception of vitamin C, which we apparently have lost the ability to synthesize for some reason... call it evolution.
I do question the nutritional content of foods though given our current environment, but we do the best we can eh?