Not according to Robert Natelson, author of “The Original Constitution”
I don’t agree totally with his conclusions, because he does, a number of times, stress the Founders reliance on Vattel.
But according to him there is no doubt that what the Founders meant was a derivation of the British flavor... a “natural born citizen” was one who EITHER:
Was born on the land (Cruz wasn’t) or
Had a FATHER who was a citizen. (Cruz didn’t).
In addition, Cruz has (or had) dual citizenship. Conflicting allegiances. That’s a big problem.
This has zero to do with whether someone likes Cruz or agrees with what he says. We can’t elect someone ineligible just because we like what they say, that’s a tactic from the other side, where the outcome is more important than the means.