I'm wondering if this "nationality" thing isn't really just a matter of how one was brought up and/or how much they know about their roots and background. I know many people who don't know what nationality they are, or they "think" their this or that.
It seems so strange that they wouldn't and like Krlea mentioned, many of them do just consider themselves American.
There have been a few times (very few here in CA), I'll find out that someone is of Italian decent, and I'll say (in my best California accent :p ) "Oh my God, so am I."
...and the other person doesn't really think it's a big deal.
TIS