Just a few thoughts: As far as the claim of "living in the best country in the world", to me this is more of an expression of contentment. I could say I live in the best home in the world. I know there are other homes out there that surpass my home in everyway, yet I am happy and content with my home so for me my home is the best in the world. I could dwell on all the negative things in my home, the carpet needs to be replaced and I would love to paint or wall paper the walls, and so and so has a bigger, newer home, to the point where I'm not happy with my home. But if I don't have the finances or means to accomplish that, there is no sense in dwelling on that now. Will fix it, when I can.
We take pride in our neighborhoods, our towns and cities, our states. There is always competion between local high school football teams.Our team will beat your team. We always compare our state's performance in everything from crime, punishments,wages sports, academic, roads and etc. with neighboring states. And whatever state you are from, you take pride in your state. Even though some other state has something better than yours. If you are truly miserable about it, you move to a place where you can be happy.
I was most impressed with a show of patriotism from some of our local WWII veterans. Many of them were Native American. Their parents and grandparents had settled our town. While growing up, they were not allowed to attend our local schools.(Sometimes I am so embarrassed to be a white person) They were shipped off the special "Indian Schools" that were miles away. Yet during WWII they enlisted in the service. Many of the tribes had treaties with the US Govt which would not allow them to be part of the military, so they had to go to court to gain the freedom to enlist. One of our Native American Vets is in his 80's now, and has been awarded the Congressional Medal of Honor.
Even though the US Govt treated them terrible, they saw it as better than what the other gov. were. They also saw it as fighting for their homeland, their country.
Our town has grown over the years, we still have a large population of Native Americans. We are a very patriotic town. We fly our flags a lot. they do the flag salute for every public gathering. There is a sense of deep pride for our community.
In closing, I don't think American are saying our country is better than yours. They are just expressing their pride and contentment with their country(not really our gov either). If you express that YOU live in the greatest country in the world, I wouldn't argue with you at all.