The paternity issue should be easy to overcome with modern technology. There's really no reason the state shouldn't require a paternity test to ensure the accuracy of the state issued birth certificate.
Some states go the other way - if you (as the father, maybe the mother but that's pretty easy to verify I hear) sign the birth certificate you are the father (Maury) for all legal purposes even if you're not - wether knowingly or not.
Some states go the other way - if you (as the father, maybe the mother but that's pretty easy to verify I hear) sign the birth certificate you are the father (Maury) for all legal purposes even if you're not - wether knowingly or not.