Evidence of what? The COLB is only prima facia (meaning at first impression) evidence of the information on it. Not everthing needed is on it. Plus, it only reflects what is in the state's database, and is still subject to challenge of that information, if there is any evidence or reason to believe that the information is incorrect or the original documents fraudulently filed. If this were a simple case of some person wishing to be recognized as a citizen, say for entry into the US, it would not take much contrary information to get the original documents, or certifed copies thereof, produced by the state which held them.
Even the long form might not be sufficient in an of itself. For example, while the long form shows the birthplace of the parents, it does not show their citizenship at the time the child was born. That might be a key piece of information in proving or disproving a case. If so, other documents would be required to prove what the parents citizenship was at the time of birth.