And in fact, it is firmly established that it's the poorest people in America who tend to be the fattest. And what free school lunches often solve is not hunger but neglect. There are lots of shitty parents who don't care enough to deposit lunch money in the school account or pack lunch for their kid, or who make appalling dietary choices for their children.
I wish people would have a little more skepticism and apply some independent common sense when consuming statistics. People getting food from food banks or consuming free lunch doesn't mean that they are otherwise going hungry. It means they are accepting something offered for free. There are myriad, complicated reasons why those patterns would change. But it's a strong, unjustified conclusion to say it's because they would otherwise go hungry.