I am from a european country, and when I had to renew my id card I had to prove my identity through answering questions about a part of my family tree my immediate family and I have been no-contact since ever. I had no idea about the names of these people, and the police officer was visibly frustrated. Nothing bad happened in the end but I can imagine if I was acting weird it could have had, because the whole id process was actually a failure.
My experience with other european countries is not much different either in terms of the process, likeprevious residence addresses, people you live with or similar info they have on you, most of which is not very private. Or a witness to testify which actually is the easiest. That's nothing that would have prevented a case like this on its own, without further investigations.