Companies could put the label "Natural" or "All natural" as much as they want to with little liability. The thing is, the USDA or whoever in charge, does not enforce anything against certain words and companies have taken advantage of that. However, the FDA/USDA or whoever in charge enforces the word "Organic" heavily.
Organic meats (such as chicken, beef etc.) does not mean that they don't contain things other than chicken but rather, it hasn't been fed with growth hormones. The majority of the non organic meats were bred and fed with the use of hormones and various other techniques.