It really seems unbelievable to me that a man can seek the presidency without providing the information requested by the plaintiffs in these cases. When I joined the Navy and required a high security clearance for my rating they took my life apart. They questioned my grade school teachers and neighbors that I hadn't seen in over ten years. They questioned my High School classmates and old girl friends. How can a man be elected president without far more scrutiny?
There are two parties with the Constitutional authority to check eligibility: the Electors prying to voting and the Congress after certification.
State secretary of states also have to follow state laws regarding access to the ballot. But they are not constitutionally required to do so.
Please not that while the electors and Congress have the authority, they are not charged with the “responsibility.” Nobody is explicitly.
In all honesty, the writing in the Constitution on this matter could have been a wee bit tighter.
There are many Constitutional issues that are never decided by the Courts. For example, there was a very serious debate as to the Constitutional legitmacy of the Vietnam War, but the courts repeatedly refused to decide it. Some issues must be decided by the voters and by the Congress. This is one of them.