The local/state law also says the candidate must be eligible for the office. It is a requirement for being put on the ballot. The issue has both state and federal ramifications. The state has an interest in ballot integrity.
My point is that the courts are arbitrary, that's all. They are willing to inquire as to certain facts (e.g., the federal requirement for AGE), making the reason they use to not inquire on NBC, not hold water.
To your point, the answer comes out different if the courts invoke standing vs. invoking jurisdiction.
Either a voter has standing, or not. If the REASON a person lacks standing is that all voters are similarly situated, that reason holds, no matter WHY an ineligible name appears on the ballot.
That answer can come out different if the REASON given is jurisdiction, then the state court is enforcing a state requirement for access to a state ballot.
I still see weaseling when the state requirement and federal requirement are the same.
Cruz essentially argues that the state has no power to deny state ballot access to a person who is ineligible for reasons expressed in the constitution. This results in a state being obliged to put on the ballot, persons who are underage or who are foreigners or who never resided in the US, etc.
The State cannot determine the NBC requirement.