He was vetted no less rigorously that any other candidate for president in recent history.
Is the vetting process good enough? In some ways yes, but in some ways no.
He's been vetted well enough to satisfy any reasonable person that he's eligible. However, I would like to see state laws passed that would make the vetting process more formal. That would leave less fodder for conspiracy theories.
It would be a very good idea if all presidential candidates were required to present proof of eligibility to at least a few secretaries of state. In Obama's case, that would mean showing a physical copy of the COLB he posted on the internet to a secretary of state.
A lot of this birther nonsense would go away if he and all the other candidates had been required to do that. There would still be some birthers out there no matter, but there would be fewer if there were a formal process in place.
With all due respect, you can't be serious. A reasonable person, if he or she is a voter or federal government worker, and takes his or her responsibility seriously, would ask for evidence that Obama is qualified under the US Constitution. The current situation is that, at a minimum, Obama is being evasive as to where he was born, and that the contemporary media is reporting conflicting information as to what country and what hospital he was born in. As to your assertion that he was vetted no less rigorously than any other recent President, whether or not that is true, it can be asserted likewise no other recent President has been as evasive as Obama about where he was born, to the extent of hiring lawyers to shield the information instead of simply releasing the information, and in any case there seems to be no other President in recent history to which the question of whether or not he was Constitutionally qualified to be President arose during his term of office (not to mention in the first weeks of his term of office).
So by the public record alone, your reasonable person test fails, since the public record yields conflicting stories about where Obama was born.
Beyond this, consider the following analogy. Let's say you are a manager hiring an employee for a critically important position your company and a requirement for the position is that a prospective employee for the position be a college graduate. You ask the employee if he is a college graduate and he responds: (1) a headhunter already responded to that, so I need not answer it here; or (2) yes, but I do not have to show you any proof since you lack standing, or (3) he declines to respond to the question. Would you or any reasonable person then as a manager conclude that that person is qualified for the position?
If I were such a manager in such a position, I would conclude that the prospective employee is being evasive and so cannot be trusted with the responsibility of the critically important position. Are you arguing differently? If so, what is your reasoning?