I read somewhere that Ascension is actually run by the companies based there?
No, though prior to 2001 the organizations operating on the island were responsible for providing common services for themselves, looked after infrastructure needs, and raised the necessary revenue among themselves to do so. However governance and the rule of law were assured by the Administrator’s Office, on behalf of the Governor. In 2002 the first elections were held for an Island Council in order to give those living on the island a say in the island’s affairs for the first time.