Exactly right.
Of course, the question then becomes who does have standing to check the Constitutional qualification of a president?
Since citizens are sovereign they have all the powers not vested by the Constitution to the government. If the Constitution does not explicitly state a government agency has the charge to check Constitutional qualifications of a candidate, then clearly the responsibility falls on the citizens. Since it is the duty of a citizen to protect and defend the Constitution, and the Constitution states that a president must be a natural born citizen, the citizens have a duty to enforce that rule.
The courts are clearly wrong on this one.
1. The U.S. Constitution is a CONTRACT between The People, The States, and The United States, the federal government, that defines and limits the role of the federal government, and the rights of the States and The People, and, among other things, defines and limits the qualifications for president, i.e., that the president must be over the age of 35 years, and must be a natural born citizen.
2. Any party to a CONTRACT has standing to enforce it. This is as basic as it gets. Contract Law 101. First week of law school stuff. And it seems that lawyers and judges all over the country have forgotten all about it. Also, the Constitution was intended to benefit all American citizens, We, The People, and in basic contract law the intended beneficiaries of a CONTRACT, i.e., us, also have standing to enforce it.
3. If We, The People, do not have standing to enforce the CONTRACT, the U.S. Constitution, then it is unenforceable, and if it is unenforceable it is just a historic curiosity that means nothing. Its just an old piece of parchment. But that was not the intent, and to give intent to the CONTRACT it must be enforceable by its parties and beneficiaries.
4. We, The People, have standing under the First Amendment "to petition the government for redress of grievances." If we have a grievance that a non-citizen, illegal alien, is running for president, I think the First Amendment unequivocally gives every American citizen standing to sue the government to redress that grievance and enforce the Constitution.