Rights are not American or not American. Rights exist even if they are violated, and are not peculiar to one place. And the rights we enjoy as Americans because they have been enumerated in various documents (which are mostly ignored today) are not granted by those documants or any laws, they come from God.
But to sum it up,
You have the right to do anything that doesn't violate the equal rights of others.
In that case he has the RIGHT to have his picture in the yearbook the same as all of his class mates. You yourself stated our rights are not limited to those enumerated.