If sprinkles-hating MeMe Roth was the national education czar, then schools across the country would be purged of everything from birthday cupcakes (replaced by birthday salads) to Halloween candy to Valentine’s Day candy-grams. But hey, aren’t all those sugary treats making kids fat? Shouldn’t schools take a hard line against all the vending machines that create a regular “toxic food environment”? Maybe not.

The American Sociological Association reports on a new study of middle school students finding that “weight gain has nothing to do with the candy, soda, chips, and other junk food they can purchase at school.” The research, which appears in Sociology of Education this month, examined almost 20,000 kids in the fifth and eighth grades. Even when snack food availability increased, the percentage of overweight or obese students decreased from fifth grade to eight grade.

“We were really surprised by that result and, in fact, we held back from publishing our study for roughly two years because we kept looking for a connection that just wasn’t there,” said the lead author of the study. Meanwhile, regulators rid schools of so-called junk food resulting in black markets for candy—“Willy-Wonka-meets-Casablanca,” in the words of one observer—and students disgusted with the new “healthy” menus.

Interestingly, a separate “surprising” study in the Journal of Nutrition Education and Behavior released last year also found no correlation between high school students’ risk of being overweight and the presence of stores with snack food choices near their schools.

Maybe it’s time for the “food police” to educate themselves. All the attempts to limit choices apparently won’t do the students any good.