So someone in the position above could continue to receive a €3000 gift tax free every year (assuming rules do not change) from an aunt or uncle, despite being now over the threshold?
€3000 from the aunt, €3000 from the uncle, and €3000 from the man next door, all tax free. It's not one €3000 gift exemption, but an annual exemption for every single person who gives you a gift.