Free school lunches and American wealth

The NYT writes about how some students who qualify for free school lunches don't take them because they don't want their friends to know they are needy. The article concludes by quoting a high school senior saying "Kids who wear nice shoes and nice clothes...don’t want to be associated with food that says ‘I’m not able to provide for myself.’"

We must live in a very rich country for how else could kids who can afford to wear nice shoes and nice clothes be classified as people from families too poor to provide for themselves.