Problem you have with that analysis is that the issue of "qualified" is not a mechanical question and it is not going to be determined by a predictable reliable process.
Whether we like it or not, the Supreme Court is a political policy decision making process. On this issue, you can argue that it should be resolved by the conceptual foundation of earlier decisions; a better argument for your view is John Jay's letter to George Washington. Neither one of those arguments is anywhere close to decisive in the current environment.
At present, the establishment bar--particularly the Constitutional Law bar; is very Liberal and very concerned about the proposition that their guy in the White House is clearly not eligible to hold the office under any theory.
There is in fact, serious Supreme Court authority that eligibility to hold office is different from procedural errors in the process of election or installation--a person who is not eligible does not hold the office. So to the extent that stands up, everything Barry has done that requires an actual "President" to do is void.
There are insider blog reports out there that one material level of establishment concern with both Trump and Cruz is that they would pursue this line to remove Supreme Court Justices and eliminate other action. Cruz continues to say regularly that he would do so.
So you have the New York Times out there telling you that it is now time to eliminate the requirement under Article II Sec. 1.
Personally, I evaluate Cruz as more likely than Trump to effectively pursue that issue and other fundamental issues that are important to me.
And as I say above, the Liberal Establishment has used its control over the process to install an ineligible, unqualified person who is determined to destroy American culture and eliminate the Constitutional Judeo Christian ethical structure of our system of government and law. If our adversaries are not going to play by the rules, there is simply no reason we should see ourselves as bound by the rules either to the extent we can avoid their application in an effort to get our country back.
But I agree, that is a close call. Like josphehm20, I am very disappointed that Cruz has not aggressively pursued getting the Natural Born Citizen issue resolved because it is in fact going to be an issue in the primary campaign and perhaps in the general election.
I hope you take no offense that I make no rebuttal. Do not take that as agreement.
One point you should research, and this is offered in the spirit of friendship, is de facto officer doctrine.