I had wondered that myself. I think in some locations it might be easier to pass a child off to someone with less official paperwork. Sometimes, I have wondered about delayed birth certificate and why the birth was recorded later.

I am aware of people going to the doctor/hospital with an assumed name or using a different persons name. A birth that happened at home would not necessarily have been recorded at the time of birth. I could see how it would be easy to create new parents on a delayed certificate.

I believe looking at the DNA might give us the answer that we are seeking though.