Based on my experiences -- decades of caring for elderly and infirm folks, and living among them -- I suspect that digging deeper into the study sample group and its references (notably one in particular*) would reveal that the at-risk demographic will have a few factors in common: poverty, age, other infirmities that hinder access to a good diet.
Typically people with those demographic commonalities will have limited access to good food, often living in food deserts where the nearest accessible place to buy food will be a convenience store, or as little as the nearest junk food vending machines.
They'll have limited mobility and transportation, limited access to health care and social services. Escalating illnesses, physical and mental disabilities, fatigue, chronic pain, etc., will conspire toward more reliance on worse and more expensive food sources -- mostly junk.
IOW, the title is misleading, putting the cart before the horse. The most significant contributing factor in cancer, heart disease, diabetes, etc., is poverty, not "diet". Access to a healthy diet will reduce other medical costs.
Unfortunately the CNN summary undermines its credibility with this sort of simplistic and misleading comment:
That may sound reassuring to the typical CNN audience who can afford to care about their diet. But it's unlikely to make a bit of difference to most folks. Having done organic gardening in my own family garden (my grandparents were way ahead of the game, back in the late 1960s-early '70s), I'd only say that those vegetables and fruits tasted better. There's little evidence or agreement among researchers that "organic" is better. Heck, the word doesn't even mean anything. "Organic" has no consensus and mostly serves as marketing fluff.
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*Zhang FF, Liu J, Rehm CD, Wilde P, Mande JR, Mozaffarian D. Trends and Disparities in Diet Quality Among US Adults by Supplemental Nutrition Assistance Program Participation Status. JAMA Network Open. 2018;1(2):e180237