Why must Muslim children only eat Halal food?

Many schools are looking at Halal options for their menus of serving all students with Halal meat but I discovered something today. Whereas Jews are meant only to eat Kosher food, it seems that the laws of Halal are somewhat less prescriptive:

"Food must be slaughtered by slitting the veins of the neck without severing the spinal cord. and the Name of God must be mentioned. Animals slaughtered for food by "People of the Book" (Jews and Christians) is also lawful (provided it's not otherwise prohibited such as pork or alcohol added)."

Is this true?