America basically comes from a latininaztion of Amerigo into Americus. A reference to Amerigo Vespucci who "discovered" that Brazil and the West Indies were not part of Asia but an entirely separate land mass. It would not have been uncommon for people in the colonies to consider themselves "American".

As early as the 17th century English colonists considered themselves American. The line in the movie is more like saying an independent nation in America. The Declaration of Independence specifically refers to the "Thirteen United States of America".

So the political entity of America is separate from American people.

Hope this helps.