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I believe that identifies that you are calling a US number
Well, yes and no. 11-digit dialing of a U.S. number will only work within the U.S. itself and, iirc, Canada (and maybe Mexico?). Anywhere else, you not only need a country code, which is indeed 1, but also the 011 prefix that indicates out-of-country calls.

More info can be found here.

Do you know the most surprising thing about divorce? It doesn't actually kill you, like a bullet to the heart or a head-on car wreck. It should. When someone you've promised to cherish till death do you part says, "I never loved you," it should kill you instantly.

- Under the Tuscan Sun