The benefit we're talking about here is food. Served in school lunchrooms. To students who are enrolled at that school. How exactly do you see this being abused?
People can only eat so much at a single sitting. Even highly-active, sports-team-member, teenaged boys. (I used to be one.) There are no massive opportunities for skimming or graft in the lunch line itself.
What could go wrong?
A child who's not otherwise likely to be in school decides to attend because they get fed. Win!
A child whose family are capable of affording a full-cost lunch free-ride. So what, that's a small fraction of total meals, make it up in taxes! (As I've discussed previously in this thread: https://news.ycombinator.com/item?id=43895455>.)
Complaints about free meals are like complaining about penny-ante voter fraud. The big opportunities aren't in showing up to polling places, as that's simply too expensive (in direct, physical-space costs). Voter fraud as a viable tactic occurs through unwarranted voter-roll purges, by disinformation about voting times and places, very rarely through corruption of counting processes (voting machines, election judges, and the like). But not by having people showing up to vote multiple times.
Sure, there's opportunity for fraud in school lunch programmes, but it's not transacted through stomachs. It's lunchroom staff skimming the till, it's vendor fraud, it's political corruption, it's kickbacks and sweetheart deals.
All of which are in fact real fraud.
But they are not identified or mitigated through means testing. Rather you want forensic audits, oversight, management practices, and law-enforcement investigating and prosecuting actual political corruption.
The kids eat either way.