But why didn't any of the attorneys filing suit ask to examine the physical document? If Obama had denied access, it certainly would have caused at least an internet storm.
The best I can say is that their cases weren't based on the authenticity of the COLB. They were arguing either dual citizenship, or lack of oversight of credentials, or failure to prove qualifications. Autheniticity of the COLB may have been in the original Berg case, but I think was amended at some point.
Since none of the cases moved past the Standing test, Discovery never happened. Examining the physical document would be a part of the Discovery process.
But I'm not a lawyer, I only watch them on FR.
-PJ