While you're not wrong about schools having the power to limit the range of speech children are entitled to employ I would caution against the equivalence of school policy violations vs actual law breaking. Sedition in US law is the use of force to hinder operations of the government. Speaking out against the government hasn't been illegal since the Alien & Sedition Acts of 1798.

That said, sure students can be punished for saying things in school, by school policy, but generally not by law, at least not speech deemed seditious or critical of an administration. Furthermore, are we talking elementary, high school, middle? At what point do kids absorb the full implications of repeating things they might hear at home or on the news?