My understanding is that in the US, it is not really possible to prove that a person doesn't exist. People move from state to state, they change names.

It's different in European welfare states which are big brother societies: you can actually get a reliable census by saying things like "select count(id) from population where alive is true;"

But this is different from proving a certain name didn't appear among the students of a particular university/class, etc; we do know the Rolling Stone story was a hoax.