Pay attention to the respect the others paid to the finder by handling his coin carefully and allowing him the honor/duty of washing away the dirt. Someone grabbing the coin and rubbing the mud with a heavy thumb could have scratched a thousand dollars away from its value. Also note when the camera man was asked and did not shoot images with recognizable backgrounds. None of those guys want you seeing that field and being able to find it. There could be a few more things there and they don't want competition.
What they are doing is perfectly legal and out in the open. UK detectorists take videos and are proud of what they find because they live in a country that allows them to find coins like this and not be sent to jail. In many places a coin found like this would already have been melted into a form that would not be traceable or confiscated as government property.