By definition:
A processed food is any food that has been altered in some way during preparation.
Food processing can be as basic as: freezing. canning.
The problem, I guess, is how manufacturers choose to process (with cheap, unhealthy additives as possible); Such that you have to buy natural just to avoid these unbeneficial decisions.In fact, I think we shouldn't even distinguish between processed/non-processed, but instead judge foods on their relevant aspects. An example of this is battery-farmed vs free-range cornfed chicken are both non-processed.