She was just being polite to the stupid Gaijin. (She would otherwise be fired in a New York minute.) Believe me: She was actually from, e.g., Okinawa.
I find it actually rather boorish to ask a total stranger such a personal question. What if they were to smilingly answer, "I wonder about that myself sometimes. You see, I was abandoned as an infant, raised by gypsies, and then sold into prostitution at the age of 13. So I really don't know."
When I bump into an English-speaker abroad, and they comment, e.g., "It's mighty cold here!" I might respond with "So where abouts are you from?" - But to speculate openly about their genetic make-up as a conversation-breaker?!
Regards,
So funny, I've done it quite a bit. Russian, Turkish, Romanian, it's very much appreciated when I get it right and engage in a conversation about their mother country.
I find it actually rather boorish to ask a total stranger such a personal question