If you are interested in actually learning about medical confidentiality, your first mistake is believing it has something to do with some legal technicality. It doesn't. It has to do with ethical patient care.
You can start here:
AMA's paper on patient confidentiality.
It's like medical practice, there is judgement involved. If I diagnose your STD and you tell me you don't want your wife to know, I am obligated ethically to tell your wife. You cannot sue me for telling her.
The parents in the OP case can easily show in court that allowing high school students to see confidential information in the morgue caused the parent of the deceased teen serious distress. The defense will likely argue the students were not just casual observers but were in a legitimate class with the morgue as a clinical. The morgue could argue the school had a duty to assure the students understood confidentiality and the breach occurred when the students told the parents of the deceased about seeing their son's brain. But since the students were likely under 18, they would not be financially liable. And if that meant their parents were, you can imagine the parents of the students would be countersuing the morgue and the school that the kids were traumatized by seeing their friend's brain in the morgue.
The morgue would be wise to settle any lawsuits here out of court if an apology was not enough to satisfy the distressed parties. It's highly unlikely the morgue would win their case in court based on some claim that the death of the friend was public knowledge.
A breach in medical confidentiality is not dependent upon some specific legal wording, it is about professional conduct and misconduct.
The reason I bolded the bit about the irrelevant medium is the labeled brain jar would be an unusual medium, but that wouldn't mean it wasn't an ethical breach.