The As don't need a written contract with Casey or Hoover to prove ownership of the tape. All they need is Hoover and/or Casey stating that they were/are working for the Anthonys. If either or both so stated at any time, then the work product belongs to the Caseys. Hoover isn't the "author" of an original piece of intellectual property, he is a camera operator producing work for the Anthonys.
Once again, this tape neither proves or disproves anything. It doesn't prove that the Anthonys requested that Casey or Hoover search any area. That is speculation, not proof. It shows a man identified as PI Casey opening garbage bags at one location and probing the ground with a stick in another location. The man is not seen bringing anything to the location, removing anything, finding anything, showing anything or in any way hiding or obscuring his actions or any kind of evidence particular to this case. There is nothing on the tape that indicates that the Anthonys were directing a search for a body. Nothing.