Having rights I believe only means that they can't name him by name. Sauron as a shapeshifter could in theory appear as basically anything (including Halbrand). Tolkien never explicitly says what race Annatar appears at.
I wish they had the rights of Annatar for RoP - and chose to have him as an elf. He was supposed to make 16 rings over a long period of time. RoP only made two and now he's exposed.