The theory doesn’t work if you don’t believe that you are more than the sum of your parts. If there is no soul, then the transportation or duplication presents no issues. But if there is a soul, and it dies when your body is shredded at an atomic level, then whatever comes out the other end is not “you”. Your soul goes on to whatever the next plane of existence is. Unless somehow the soul is also able to survive the transportation event, in which case it’s fine. The issue Bones and others like him had is that they didn’t believe that the soul survived the event.