Is the US part of the EU?

A non-tech-related post. Jeff suggested I post my funny experience from my last trip to the UK. I've landed at Heathrow airport in London and got to the passport control area. There are 2 lines: a short one for Europeans (EU and European Economic zone), clearly marked, with a list of countries and flags, and a longer one for rest of the world.
I whipped out my European passport (useless most of the year - only saved for days like this) and strode to the shorter line. But pretty soon I felt there was a snag in the line: the other one actually advanced faster. I looked over the shoulder of the woman in front of me and heard the following sentence: "sir, the US is not part of the EU". A man was trying to argue with the girl at the counter. He desperately looked at the long line to the right and asked the girl: "do you expect me to go to the end of this line?", to which she replied, with the same tone as before "sir, the US is not part of the EU".
After some more grumbling, he took his bag and moved to the end of the other line. The girl then asked "is there anyone else from the US in this line?", I looked behind me, and at least 3 other passengers were raising their hands...