those issues not in question in the challenge at the hearing.
A State cannot make a decision pursuant to something far beyond their purview - a determination of Constitutional eligibility for a Federal office.
They can only determine if he met the eligibility requirements for the State of Georgia.
That could (and should) include proof of citizenship at birth in the form of a certified copy of a birth certificate sent from one SOS to the ballot issuing State's SOS. But absent such a legislative requirement - the judge and SOS have to determine the law as it is written - not ‘how it should be’.
Thus the language of the SOS was that 0bama met the eligibility requirements, not to be President, but to be on the Georgia ballot.