Could FAA's Drone Policies Violate the First Amendment?

Could the FAA's drone policies violate the First Amendment?, TechDirt's Mike Masnick asked in a post on Christmas Eve, citing a post from law professor Margot Kaminski. If the FAA can authorize Hollywood to use drones for commercial purposes on a pilot basis, why can't other drone operators fly their machines wihtout restrictions? "'The Supreme Court has long acknowledged that a too-discretionary licensing regime can raise serious First Amendment concerns. This is true even where a complete ban might be permissible,'" Kaminski noted.