Hi, I am an Argentinian. While in Spanish the word "americano" means that you were born somewhere in The Americas, in the English language the word "american" means that you were born in the USA (AKA: America).
It happens a lot that words which are quite similar mean different things in different languages. Let's just embrace and understand these differences.
Cheers!
The big problem with this word is that, being USA as influential in the western culture as it is, it helps corrupting the corresponding word in the languages that do have a proper gentilic like French and Spanish. Also, it promotes ignorance among the ignorants (I've met US people thinking America is just and only the country) without a tangible benefit.
See http://users.dcc.uchile.cl/~rbaeza/inf/american.html for a similar view.