No, obesity is not just the schools' problem, but the problem of the United States as a whole. Though schools can play a part in determining a child's health education and what a child eats, it also stands that unhealthy food is cheaper than healthy food, so a child eating unhealthy food is more likely.
Schools always push for students to be prepared for the 'real' world by punishing them severely for stupid things such as stepping out of line, making gun shapes with your hands, and demoralizing them and removing the rights they were born with. Well, having unhealthy food in the cafeteria is simply an introduction to how life is in the real world: fast food everywhere. It is up to the parents to raise their kids feeding them healthy foods. For example, I never drank soda as a kid. As I grew older, I still never felt that I needed to. If kids are taught properly by parents, there should be no problem with what they eat at school.