Who doesn't love to learn a little bit about their family history? After all, most people who live in the US do not originally come from the US (unless you have Native American heritage). As a melting pot of cultures, people are always eager to talk about their heritage and their ancestry, claiming to be Italian or Irish if they have just one person in their ancient family history that came from there.
It may come across as offensive if an American is traveling to Italy and claims to be Italian when they really just have one great great great grandparent who was born there.