Yanks are cool, leave 'em alone.
Of course they are gonna get shirty if you belittle or ridicule their country, just as you would if they did the same to you.
I have never left Australia, so I don't know what it is like anywhere else, but every American I have met around here has been polite, quiet, helpfull, generous and very complimentary about my country and countrymen.
They are proud of their nation, as they have every right to be, by any measure it is a great country.
They have also, to a man, stated if I ever get to their country, that they would be more than happy to put me up for a few days, show me around etc.
Many, upon finding I have a sister living in the US, and that I will get over there to see her and her adopted country some day, have given me phone numbers and addresses to contact them if I happen to be in their city/county/state.
They are fascinated by our country, it's wildlife, it's scenery and it's people and their ways.....I only hope that when I do get to travel, that I can be as good an ambassador for my country as they are for thier's when over here.
If it came down to, as you put it 'USA vs. The World', I have no doubt what side of the fence I would be on, and it would be rather short on croussaints and big on hamburgers.
(BTW reffering to Europe as 'the rest of the world' is way more arrogant and just plain wrong than Americans saying the US is great......what about Asia, Africa, Australia/NZ/Oceania, India? thats a whole big chunk of the 'rest of the world' being ommited there)