You have way too much confidence in high school kids. Let's face it, they are still kids. I don't see what's so wrong with this. As long as the kids live at home, the parents should have a say in what the kids eat, what they wear and so on.
You just said it. The parents should have a say and when I was a child they DID. It's a thing called obedience, a thing that is sadly lacking in many children today. An obedient child will not eat foods that his/her parents specifically prohibit and will not eat more of a food than allowed by his/her parents.
If a child is not obedient, then the child may have some sort of behavioral psychosis. Otherwise, the parents are just simply failing at raising obedient children. My parents didn't need a fancy lunch item authorization system. If they said to eat dirt... I ate dirt. When I was old enough that I was unwilling to follow their rules I was old enough to move out and make my own way in life. Of course my parents would never have asked me to eat dirt or do anything else that was clearly not good for me.
Mine were loving parents and I think that's key to successfully instilling obedience. Children are a lot more likely to be obedient when they know that their parents are making decisions in the child's best interest, even when the child doesn't really understand. A loving parent will normally have children who trust them to make decisions both in the child's best interest and with wisdom that surpasses that of the child. If your children don't obey you except when you're present, then you're doing something wrong. If you have serious doubts as to whether or not they obey you when you're not present, again you're doing something wrong.