I think the paleo diet did not originally include grains because the people were "hunter/gatherers" so they ate what they could find; grains as we know them today did not become popular until people actually settled down and began growing their own food.
Of course, the closer you get to fresh foods the better. That's why we recommend that you shop around the "outside walls" of you supermarket. Just think of the lay out produce, dairy, fresh meats are all along the outside walls; the closer you get to the center of the store, the more processed the foods will be -- check it out next time you go shopping.
Of course, fresh fruits and veggies should be a large part of your diet, but if don't keep it well rounded, most likely you won't stick with it.