The other important part of this policy is that it normalizes kids not paying for lunch. This is important because they realized many kids who couldn't afford lunch were still skipping their free lunch because they were embarrassed to get a free lunch. When everyone gets a free lunch then nobody is embarrassed.
I've heard of some schools going out of their way to make it obvious which kids were receiving free lunch and which weren't; however, that wasn't universal to all programs.
Our school just had "lunch tickets." There was a register on a different floor from the lunch room where you could go buy them, pick them up if your parents bought them by check, or pick them up if you were on the assistance list. Once you had them they were all the same. Only the person at the register would know your status.
None of my friends who got that ever were embarrassed in any way about using them as they were the only ones to know.
