Well, consider: someone who is documented as dead appears with a birth certificate. Do you a) assume that this person is the (presumably) deceased person, or b) assume that a living person is trying to steal a deceased person's identity?

The problem is that we're really poorly equipped to handle problems of identity. It's hard to prove that you are you, absent documentation. Documentation usually issued by a government, or by a private agency on behalf of a government. And if that government thinks you're dead, well, all that documentation is worth about as much as the paper it's printed on.

Short of, say, a dental, medical or DNA match, then yeah, this is a really hard procedural fix.