…Be allowed to enforce a politician’s verbal restriction against making a video of him at an open meeting?
Politicians are supposed to represent the people. Therefore, when they talk in public they should be expressing ideas favorable to the people. If they do not want to be videoed it becomes suspicious as to whether or not the politician has something to hide.
As an individual the politician does have the right to not be videoed, just as much as you or I do. However, while performing his job as a representative of the people, they should be able to see and hear him nation-wide.