Neither would apply here. State/local courts don't contol Federal elections. The 14th Amendment deals with who has citizenship and the power to vote, not qualifications to run for office.
Section 1 deals with the qualification to run for president and all it says is "natural born citizen". I say he is one. Maybe you says he's not. Fine. Let him run. Let SCOTUS do their job (for once). They can rule and then we'll all know.
The only federal election law is campaign finance law. The states control ballot eligibility. That is why Obama’s eligibility was challenged in about 30 different states in either 2008 or in 2012. The Chief Elections Officer (usually an elected Secretary of State) controls who is eligible under each state’s election laws with challengers having the right to file suit or appeal to state Elections Boards.
The Supreme Court did do its job, more than 100 years ago and the current court has simply let precedent stand and refused to overturn settled law.
For example, in 1898 the Court ruled in United States v. Wong Kim Ark:
[An alien parent’s] “allegiance to the United States is direct and immediate, and, although but local and temporary, continuing only so long as he remains within our territory, is yet, in the words of Lord Coke in Calvin’s Case, [7 Coke, 6a,] ’strong enough to make a natural subject, for, if he hath issue here, that issue is a natural-born subject’
“Subject’ and ‘citizen’ are, in a degree, convertible terms as applied to natives; and though the term ‘citizen’ seems to be appropriate to republican freemen, yet we are, equally with the inhabitants of all other countries, ’subjects,’ for we are equally bound by allegiance and subjection to the government and law of the land.’
and
“…every child born in England of alien parents was a natural-born subject, unless the child of an ambassador or other diplomatic agent of a foreign state, or of an alien enemy in hostile occupation of the place where the child was born.”
“The same rule was in force in all the English colonies upon this continent down to the time of the Declaration of Independence, and in the United States afterwards, and continued to prevail under the constitution as originally established.”
Current U.S. Law {8 USC 1401} covers Senator Cruz’s birth circumstance. A “Citizen of the United States at Birth” includes: “g) a person born outside the geographical limits of the United States and its outlying possessions of parents one of whom is an alien, and the other a citizen of the United States who, prior to the birth of such person, was physically present in the United States or its outlying possessions for a period or periods totaling not less than five years, at least two of which were after attaining the age of fourteen years:” That covers Calgary, Canada-born Senator Cruz, his Cuban born father and his Delaware born mother.
There is no current distinction in law between a Citizen of the United States At Birth and a Natural Born Citizen. The terms are synonymous.
But yeah, we're so much smarter than our founders. We know better what they really meant.