Speaking as one of them:
Taking my passport as an authority, it says:
Nationality: UNITED STATES OF AMERICA
The problem, of course, is that the name of the country is "United States of America," which is too long to be a convenient modifier and almost cries out for a convenient abbreviation.
If you were filling out a landing card, putting "USA" in a blank for "nationality would not be unusual -- as suggested by jpyvr
In your sample, however, I would write it:“The most common nationality was U.S...." (with periods, BE:full stops).
Actually, all of the above work and the specific usage depends somewhat upon context.
I don't quite share Brioche's comments on "Americans," not that it's wrong, but it's no more "correct" than "U.S" or "United States" -- and is longer to write than just "U.S."
I wouldn't worry too much about it.