Is this not how it works? I'm not Muslim, this is what I understood from a Muslim coworker. He also implied that there's some politics involved, in that various Middle Eastern countries align themselves with their political bloc when announcing the day, although any political motivations are "alleged" and not acknowledged.
There are no central authorities, only a menu of organizations and traditions that one can choose from. In some cases there is social pressure to choose one, and that social pressure is sometimes intense enough so that it feels like there is a central authority.