In many states, juvenile proceedings are confidential. A prosecutor cannot divulge anything unless there is a waiver and, in some states, perhaps not even then (confidentiality non-waivable). That aside, a prosecutor has to be careful about what he or she says about a pending case.
Some courts do not allow video cameras into courtrooms and, even where they do, this does not usually extend to juvenile proceedings. This may be the reason for the arrest threat because the reporter wanted to take a camera to the third floor, presumably where the hearing was being held.
Having said that, attempting to get a gag order in this type of situation involving free speech seems thuggish and stupid. I'm thinking the prosecutor is feeling some public pressure while being squeezed from the other side by the police and school authorities.