family stories: switched at birth

this is the story that my mom told me about her paternal grandfather:

There were two women who gave birth at the same time at the same hospital. One of the mothers died; the baby of the other mother died. So the ?nurses? switched the dead baby to the dead mother, and gave the live mother the live baby...

So that although I can do the genealogical research, without DNA I won't know FOR SURE how far that line goes back...