It would be his right. I think a lot of people praising this kid are failing to realize how separation of church and state work. The school can not lead a prayer during a graduation ceremony. It is a school function and a prayer led by school officials violates the entire premise behind separation of church and state (public school only obviously). This kid however is welcome to pray in his seat, in the stands, during his speech, whatever. Even being valedictorian doesn't make him an official of the school and thus an official of the state, it's just an honor bestowed upon him. His speech is perfectly welcome to contain religious references if he chooses.
Notice how it talks about him ripping up his pre-approved speech but it nowhere mentions him ever trying to get a version with the prayer approved to begin with. It probably would have been. The only thing schools would generally disallow would be profanity or verbal attacks on the school or students, they may also disallow speech with a clear political agenda as a graduation speech is no place for such a thing.
This is what I was going to say. I don't see why anyone would want to punish him (though I wonder if he was hoping to be made a sort of martyr?).
If I were a student there I would object strongly to the school officially bookending my graduation with a religious reading (that I would not identify with or see as having anything to do with my graduation) - but if a student wants to read something like that as his own 'speech', what's the problem?
Personally, I wouldn't mind if a student gave a political speech either (within reason). Its their speech, I expect nobody other than their own family is listening anyway.