Public Advocate Letitia James says the school system is out to lunch as it worries about unanticipated costs in a popular plan to provide all public school kids with free meals. Her claims don't ring true.

But that didn't stop her from making schools Chancellor Carmen Fariña swelter in the hot seat this week at a City Council hearing.

Fariña told the council that universal free lunches in the New York system might inadvertently cause the city to lose part of its federal school-lunch money -- which subsidizes meals for children from impoverished families.

If she's right, the city could be on the hook for way more than the $24 million advocates say the program will cost.

"You just don't get it," James told her.

We're not sure James gets it. And we're not sure Council Speaker Melissa Mark-Viverito, who expressed her annoyance with the school system, does either.

Here are the facts: A universal program would serve lunch to all of the city's 1.1 million public school students. Right now roughly 75 percent are eligible for the federal free-lunch program. But not all eligible families have signed up. Why? Because some parents may not want to concede they need help. Because some parents may be here illegally and afraid of trouble. And because some kids may come from hard-to-track homeless families.

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But if too many eligible kids remain outside the federal program, the city could end up paying the tab for them. Meanwhile, the city also worries that a universal program could change the way eligible kids are counted -- harming New York's ability to collect federal reimbursements.

For a school system with a $20-billion operating budget, the estimated cost of $24 million may look like a rounding error. But miss the mark and we're talking real cash.

Fariña is right to be cautious. The free-for-all program is a strong idea. It would end the stigma for poor kids in the lunch line and help struggling parents. But the city must make sure it fully understands all the costs involved.

And it should not feel compelled to jam this idea into the budget that takes effect July 1. James and the council should not turn free-for-all into a food fight.