It is when it is being used as a generic name for a school within the public school system , which it obviously was in this case. Since you seem to be a grammer expert, let me ask you this ... If your parents had named you 'Public School Smith' would you find the captialization of your name 'Public School' to be proper or improper?
BTW, you seem to be convincing me of your lack of comprehensive skills. You also seem to be lacking an attention span necessary for the continuing development a discussion about this article. You seem to think it's about grammer and not about the original topic of an Indian tribe court motion before the 9th Circuit. Or about my post to you pointing out that it was the Indian Tribes, not the court, that made the motion to prevent the study of the bones. Something you seem to either wish to ignore or can't understand by reading the article.