I think he means America does'nt exsist by saying it was Colonised by British and so so many immigrants like Polish,Italian,German,Scottish,Irish,etc all moved to America for a better life and therefore some Americans believe theres no such thing as an American.
If you google the American Melting Pot it will help you
Sounds like Ms. Beecher was trying to say that people around the world see America as a wonderful, free country. Where dreams come true. People often talk about the American Dream. And how anyone can make it happen. But trully America is swamped in debt, homeless people, and familys torn apart by natural disasters. That yes, America exists, but not the America people want to exist.