I think only way the argument makes sense is wit fixes and variable costs. If the money per student that is leaving includes some of each students share of a public school's fixed costs, then the public school will still have the same fixed costs with less funds to be allocated to it, because fewer students = less dollars.
However, if the cost per student is only a measure of the variable cost of each student to the public schools. Then, in no way should it affect the public schools.