"Under the laws that apply at the time" is an important caveat. We should do away with birthright citizenship and put an end to anchor babies and maternity tourism. If Maria slips across the border to deliver her baby in San Diego, fine, but the kid should remain Mexican, not American.
An ancient history detour. Cruz may be a sharp academic debater, but he missed a winning response when Trump raised the citizenship issue in the debates. Cruz made the intellectual's mistake of actually answering the question asked, which has never been the right way to debate someone like Trump, who is not tied to logical argument and who speaks elliptically. The way to answer a showman is with a better story.
When Trump raised the citizenship question, Cruz should have laughed and, with a big grin on this face, said: "Donald, before answering that, and just for the record, my family has been in this country a lot longer than yours." You can wordsmith it from there, but the fact is that Trump's mother was an immigrant, as was Cruz's father. But both of Trump's paternal grandparents were born in Germany, so Trump is only a second generation American on his dad's side. Cruz's maternal forbearers were a mix of mostly Irish and Italians coming over in the mid 19th century, but one strand of Cruz's family runs back in America at least to the early 18th century. Cruz should have had some Scots Irish frontier folklore at his fingertips.
From the standpoint of the rhetorical autopsy, Cruz spent too much time rooting his story in his dad's experience. This made sense in terms of the fight for freedom stump speech that was his bread and butter in the primaries. He would have been well served, however, to summon up other ghosts as well. Had I been advising him, I'd have suggested that he make a joke about how Trump would look good about as good in lederhosen or a kilt as he himself would look in a toga, so thank God we're all Americans. Or about how he'd spot Trump haggis and weinerschnitzel while Cruz could lay claim to pizza, fajitas and leprechauns. Conclude by saying, "But mostly I'm glad that we're Republicans so we don't have to play tribal identity politics like the Democrats. We're all Americans." Repeat it once in Spanish and then, "But bottom line, to answer your question, some of my ancestors were in this country 300 years ago, Donald. You're the newcomer on this stage."
Granted, this would not have directly answered the point Trump was making, but Trump wouldn't have known what hit him. I don't imagine that Cruz would challenge Trump for the 2020 nomination, but if he did, I hope he could find an ancestor who was with Washington at Valley Forge ... in response to your lurking citizenship question. His family has been here long enough for that.
One is a natural born citizen because ones comes by that citizenship naturally, no law is needed.
Naturally one could only be an American citizen when one is born here of citizen parents.
When one has a foreign national parent or parents one acquires other nationalities and is no longer naturally an American.
The purpose of the natural born citizen requirement was to insulate the office from any foreign influence, John Jay said so in a letter to George Washington that still exists.
Children of foreign nationals born with divided nationalities, loyalties and allegiances were exactly who the founders were excluding.