By analogy, do you consider each of the Major League Baseball teams to be "completely independent" businesses? Of course not. They are connected by contracts, play by the same set of rules, share player drafts, are governed by a common commissioner, share televison revenues, etc. Certainly there is a degree of autonomy in running their individual programs, but the supreme entity is MLB, not the individual teams.
Not really.
Your ideas are completely independent of logic and law, and are connected to each other only by the source from which they emanate.
Oh, this is fun, let's try another example.
France, Germany, the United Kingdom and the other members of the European Union are completely independent, and are connected to each other only by a league.
They share a common currency, the Euro. Citizens of the EU can seek employment in the territory of any EU member. Well, isn't that special?