I don’t think that she means it as literally as you are interpreting her. It’s a _feeling_ of not belonging to or probably feeling welcomed to join the culture that surrounds her daily life, I don’t think she cares whether she belongs to the history-based definition that you outlined of modern “synthetic” unified Germany.
This experience is usually invisible to the people who are part of the in-group, in this case Germans, but if someone lives in a foreign country for an extended period of time and tries to make it their home, I think they understand what that woman was saying.