That is correct.<quoted text>
The School District prohibited him from reciting a prayer. What a wonderful life lesson from the valedictorian of his class. "I shall show my classmates how to disrespect authority". He should have been denied his diploma.
The Constitution protects against illegal searches and seizure as well. That doesn't apply to students on school property. Students' lockers, backpacks and pockets can be searched at any time.
That's a different question than whether the school can permit or encourage voluntary prayer and so forth.