Any school is eligible to receive NSLP for its students; meals come from a number of different sources, they can come from on-site production, vended meal from a NSLP caterer or in most schools provided by the local school board centralized kitchen.
This is usually regulated by each state's Department of Education's nutrition services. Regardless of who provides the food (on-site production, catered-vended, or school board kitchen), the raw materials come from USDA as donated commodities; in the case of vended meals, the caterer must use and credit the school for the commodities received.