The AARCO (Assocation of American Feed Control Officials) has said that the word natural cannot be used on a pet food label if any of the ingredients are chemically synthesized. HOWEVER, and this is important, if the vitamins and minerals are chemically synthesized, the label can read "Natural, with added vitamins and minerals."
You also need to know that the list of preservatives listed on the label of your dog's food may not be complete! Meaning, that pet food companies are only required to list the preservatives that they add to the food during processing. This means they only have to list only the ingredients in their recipe.
One more thought to ponder before I leave you is the use of the "variable formulation". This means that the manufacturer can slightly change the food's recipe from batch to batch, depending on the availability or price of the ingredients. This would be why your dog may do well on one batch and then not the other.
Interesting and scary information, isn't it?