Geographically correct or not, whether it can be used by nationals of any other country on this continent or not, American is still correct.

In all other countries, citizens of the U.S. are referred to as 'Americans.' In fact, people on the street will ask you if you are German, American, English, etc. It is the common term used worldwide. Also, it is used in most references as well:

http://kiev.usembassy.gov/amcit_misc_dualnat_eng.html
http://www.puertoricousa.com/english/history.htm
http://www.wave.net/upg/immigration/resource.html

Cia World FactBook:

United States
Nationality:
noun: American(s)
adjective: American

https://www.cia.gov/cia/publications/factbook/geos/us.html

According to Theodore Roosevelt:

But if he is heartily and singly loyal to this Republic, then no matter where he was born, he is just as good an American as any one else.

The one absolutely certain way of bringing this nation to ruin, of preventing all possibility of its continuing to be a nation at all, would be to permit it to become a tangle of squabbling nationalities, an intricate knot of German-Americans, Irish-Americans, English- Americans, French-Americans, Scandinavian- Americans, or Italian-Americans, each preserving its separate nationality, each at heart feeling more sympathy with Europeans of that nationality than with the other citizens of the American Republic.

The men who do not become Americans and nothing else are hyphenated Americans; and there ought to be no room for them in this country. The man who calls himself an American citizen and who yet shows by his actions that he is primarily the citizen of a foreign land, plays a thoroughly mischievous part in the life of our body politic. He has no place here; and the sooner he returns to the land to which he feels his real heart-allegiance, the better it will be for every good American.


Encarta Encyclopedia:

It was therefore an important precondition for the rise of an independence movement and the subsequent emergence of a unique American nationality.


The U.S. Declaration of Citizenship for Winston Churchill:

BY THE PRESIDENT OF THE UNITED STATES OF AMERICA
A PROCLAMATION

WHEREAS Sir Winston Churchill, a son of America though a subject of Britain, has been throughout his life a firm and steadfast friend of the American people and the American nation;


Winston's response:

Mr. President, your action illuminates the theme of unity of the English-speaking peoples, to which I have devoted a large part of my life. I would ask you to accept yourself, and to convey to both Houses of Congress, and through them to the American people, my solemn and heartfelt thanks for this unique distinction, which will always be proudly remembered by my descendants.


From the International Labor Org:

the United States
the United States of America
(of the) United States (of America), American




>I was watching my favourite intellectual quiz show last week: "QI", and one of the questions was "What is the nationality of a person from the USA?". I kinda missed the answers. Now a lot of them would say "American" but that essentially refers to the continent; a Canadian could equally call himself "American" (as indeed could a Mexican, Bolivian or Chilean - "North" or "South" aren't included).
>
>So what is the nationality?