Sorry, but that's incorrect.
1) The
United States does not formally
recognize dual citizenship. However, it also has not taken any stand against it, either legally or politically. Typically, no
American will forfeit his or her
citizenship by undertaking the responsibilities of
citizenship in another country.
source findlaw .
2) i would also point you to the actual oath of citizenship of which i am very familair, you will notice you have to swear off all allegiance to any other country when you do so.
Oath of Allegiance I hereby declare, on oath, that
I absolutely and entirely renounce and abjure all allegiance and fidelity to any foreign prince, potentate, state, or sovereignty of whom or which I have heretofore been a subject or citizen; that I will support and defend the Constitution and laws of the United States of America against all enemies foreign and domestic; that I will bear true faith and allegiance to the same; that I will bear arms on behalf of the United States when required by the law; that I will perform noncombatant service in the armed forces of the United States when required by the law; and that I take this obligation freely without any mental reservation or purpose of evasion, so help me God. A simple version of the oath would read: I swear that I will not be loyal to any other country. I will support and defend the Constitution and laws of the U.S. I will defend the U.S. from enemies outside and inside the U.S. I will bear arms, carry a gun or fight, for the United States if asked. I will do non-fighting work for the military if asked. I will do important work for the country if asked. I take this oath freely and with out any doubts.