If a trial comes about for murder of the baby, either the defense or the prosecution (or both) may need the video to show what condition the home was in, what was in the home and at what time period, the home may also be searched again, therefore this video is evidence. This video was filmed after LE was there, either side could need it. The film may be in possession of the media, but the Court may deem it necessary to properly defend or prosecute to show what is in the film. The film then belongs to the Court via subpoena, and any further Courts that may need it for Appeals, Habeas, or anything further.
I still have no idea why you think the family's defense attorney would be called to testify about a news video. I'll believe it when it actually happens.
JMO