Re: Brexit will never actually happen
Check your passport and tell me if it doesn't say "European Union" anywhere on the front cover. If it does, then yes, I'd say you missed something.
As another example of the kind of suite of institutions that comprise the EU, you may have heard of the Common Fisheries Policy? The Council of Ministers was advised that the Treaty of Rome did not give any authority for the CPF to operate, yet they continued with it and failed to admit this to member states. This was only sneakily corrected twenty years later in the Maastricht Treaty.