I'm not saying it would; I'm saying it potentially could.
But the CC system also provides anonymity, since most cards used for fraud are stolen anyway, so the fact they're tied to a real person is irrelevant.
Bitcoin, on the other hand, doesn't suffer from the same problem as CC - that the payment info must be shared with every single merchant - so it's potentially must harder to steal; Target wouldn't have a copy of your bitcoin wallet just because you bought something from them, for example.