Edit: the threat of violence is obviously not acceptable in an age of horrifying events like school shootings. I think that goes without saying, but wanted to add to my above comment. As I unfortunately didn't make it super clear.

However, there should be a way to address the risk and prevent acts of terrorism without turning into a police state. A more reasonable response might have been to have the parents come by for a long meeting with the principal, school counselor, and school resource officer to talk about the severity of making such statements - even if she did make it sarcastically as tone/intent is difficult to judge. Then suspend the student for a day or so and have the school resource officer periodically check to ensure she didn't bring any weapons.

To play devil's advocate though, I can't imagine the stress from parents who have children of Mexican descent in such a situation.