I think this actually means that Tom hanks and his wife now have Dual citizenship

However, there are a lot of advantages to this because Greece is a part of the European Union which allows them to have a home in Greece (or any other EU country) while still maintaining their U.S. Citizenship too.

The way the U.S. is such a disaster area because of Trump, being able to go somewhere more sane when you need to might be useful to many people.