Are the people that sign the birth certificate the legal parents

Not necessarily... if a man comes forward claiming parenthood... and the DNA test proves he is... the guy on the certificate is going to have an uphill battle... and anything a court proclaims supersedes whatever is on the birth certificate. And that includes cases of adoptions as well. Just because a name is on a piece of paper... doesn't it's the end all beat all.

Depends on where you are. In some areas only the doctor signs the certificate. If your area requires parental signatures, then they would be considered the legal parents until a court rules otherwise,