You are correct, of course, and the school could win this one by having a credible military representative confirm its decision.
Even worse for the students, it could be the school official is such a military vet (although without further info, most of us with good reason would quickly speculate it was an anti-American liberal).
Uhuh, then why claim it was a safety issue? That’s the same kind of BS a school used to keep American kids from wearing shirts with the American Flag on them. If the issue was being disrespectful they should have said that. Funny though, so many people accept the defilement and destruction of the American Flag as free speech, but flying it from your truck doesn’t merit the same protection.