The original story had nothing to do with a child turning down a free lunch. It's about a kid, Maurice Mazyck, who met a private benefactor, Laura, asking to literally have his lunch placed in a brown paper bag:
“Look, Maurice, I don’t want you out there hungry on the nights I don’t see you, so this is what we can do. I can either give you some money for the week–and you’ll have to be really careful about how you spend it–or when you come over on Monday night we can go to the supermarket and I can buy all the things you like to eat and make you lunch for the week. I’ll leave it with the doormen, and you can pick it up on the way to school.”
Maurice looked at me and asked me a question.
“If you make me lunch,” he said, “will you put it in a brown paper bag?”
I didn’t really understand the question. “Do you want it in a brown paper bag?” I asked. “Or how would you prefer it?”
“Miss Laura,” he said, “I don’t want your money. I want my lunch in a brown paper bag.”
“Okay, sure. But why do you want it in a bag?”
“Because when I see kids come to school with their lunch in a paper bag, that means someone cares about them. Miss Laura, can I please have my lunch in a paper bag?”