I believe it. Any Italian grocery store will have whole aisles dedicated to "merende" or snacks for kids. These don't include the crisps. They are sugar-laden higly processed snacks. I moved to Italy in '96 and until last year, saw kids getting heavier while I also saw more fast food restaurants opening. The kids are also so controlled it's hard to see any running around free just playing. I can't tell you how many times I've heard mothers yell at their kids to stop running because they might sweat (and therefore catch a deadly disease and die ). In fact, it has become a joke in our Italian-American family to randomly yell at each other to stop sweating.
I moved to Norway where most kids are allowed to have sweets once a week, they spend all their time outside running around (even in freezing weather), and the grocery stores have a tiny area of processed snacks which don't seem popular at all. I have hardly seen any overweight kids here.