@reasoning logic,
I'm glad you're enjoying it, it is a brilliant series. That woman with the megaphone, popped onto my screen just before I was going to bed. I did try watching it, but called it a day when I realised that's all it was. If someone has to shout their message at you, it's not really worth listening to.
What difference does it make whether or not America is completely legally independent of the UK? What matters is reality, if you look at recent history America calls the shots. America got the UK to back out of Suez, America got the UK involved in Afghanistan and Iraq.
The only instance where the UK put pressure on America was Kosovo, and then it was because Blair gave a speech to the American people who then put pressure on Clinton.