There are hacking operations, there are hacktivists, but yes, there is no official organization structure. It's just a global collection of individuals who freely operate together on various hacking efforts, that anyone can join in on if they know where to look. It's more like a society with no command structure and no requirement for consensus on everything, just an underlying common creed. It's individuals cooperating through a cyber-marketplace of ideas, and anyone who claims leadership is a phony.
RE: An offer to the Anonymous group