No, because
A) The prevalence of Highly Palatable + Nutrient Deficient Food didn't simply happen as a single discrete event in 1982. It started in the 40s and has gotten progressively worse through the present time and It Is Still Getting Worse today. I live in a rural community surrounded by actual farms where the small town grocer is in danger of being put out of business by the Dollar General that opened up several years ago. If that happens it will be a 30 minute drive to get fresh vegetables or meat. This is a common story in rural and urban communities alike. IOW this is not a static problem.
B) Individuals don't get fat overnight when the food environment changes. The genetically very lucky don't get fat at all, while the genetically screwed get fat almost immediately, and a lot of people in between the two extremes get fat slowly, thus titrating into the societal obesity percentage over time.
C) Delayed second-order effects. Crash diets and fad diets, many of which are shown to make people who try them fatter in the long run. Social stigmas which result in chronic low-grade eating disorders (like eating McDonalds in your car instead of going inside where people are). "Diet" versions of foods and sodas which like fad diets may do more harm than good in the long run. Bad habits learned in childhood. These things can take a long time, a generation or more, to get 'baked into the cake' if you will.
I don't think anybody is saying Highly Palatable Food is the only cause, either. But a gradual increase in aggregate obesity ###s over a period of time when the food environment has been steadily deteriorating is perfectly consistent with just about any reasonable causal coefficient you care to attribute to the food.