Consider a situation in a US public school where a bystander/observer of a fight records that fight with their cell phone. If the fight was interrupted by a person of authority, is that person of authority allowed to search everybody's phones and delete the video? Also, are the bystanders subject to punishment?
Assuming US public schools, schools may be able to confiscate cell phones, if they prohibit cell phone use during instruction hours (a common rule). The 4th Amendment may prohibit them from searching the phone: nothing authorizes a school to delete files from a phone. Whether they may search would primarily have to do with urgent safety concerns. Schools have broader authority over students because they are acting in loco parentis, but that is distinct from carte blanche (especially since the courts now recognise that school attendance is mandated by law, thus intrusions on constitutional rights receive narrower scrutiny). Warrantless searches are allowed, based on a "balancing" of the item searched, the infraction, and the quality of the suspicion (New Jersey v. T.L.O).
One of the problems is that there is a certain baseline of expectation of privacy against which searches are to be judged, but, frankly, teen-agers have highly variable privacy expectations (Safford v. Redding). Courts recognize a reasonable expectation of privacy in terms of content on cell phones (Ohio v. Smith). This article is about the question of student cell phone privacy rights.
The general pattern, I have to say, is to start with the assumption that the school has a particular right, so they do something, and the student sues until the state or US Supreme Court articulates principle recognizing the student's constitutional right, at which point districts change their behavior. Based on existing case law, I would guess that this would be found to be an unconstitutional search, and is unlikely to actually happen (unless the district doesn't effectively communicate the law to staff). Deleting content would be beyond the pale.