Absolutely not true. Before our country was founded, the term natural-born in England included citizens born outside the country to English citizens. That is the common understanding at the time. No part of the term "natural-born" has any reference to geography. If they wanted it to mean citizens born on U.S. territory, they would have said so. By not writing anything about geography, the Constitution therefore includes anyone who is born an automatic citizen, like Cruz.
Not to mention, since you only have to be on U.S. soil for 14 years to be president, no matter your age, the founders obviously weren't obsessively concerned about your geographical location.
https://en.wikipedia.org/wiki/Natural-born-citizen_clause
The use of the phrase "natural born" was not without precedent. Statutes in England prior to American independence used the phrase "natural born subject". For example, the British Foreign Protestants Naturalization Act 1708:[10][11]
The children of all natural born subjects born out of the ligeance [i.e. out of England] of Her Majesty Her Heirs and Successors shall be deemed and adjudged to be natural born subjects of this Kingdom to all intents, constructions, and purposes whatsoever.
It so good that people here want to talk about what the US Constitution says about who can be president, so let’s get right to it:
The United States Constitution.
Article. I.
Section. 1.
All legislative Powers herein granted shall be vested in a Congress of the United States, which shall consist of a Senate and House of Representatives.
Section. 8.
Clause 4
To establish an uniform Rule of Naturalization, and uniform Laws on the subject of Bankruptcies throughout the United States;
Article. II.
Section. 1.
Clause 5
No Person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President; neither shall any Person be eligible to that Office who shall not have attained to the Age of thirty five Years, and been fourteen Years a Resident within the United States.
(1A)
No Person except a natural born Citizen, at the time of the Adoption of this Constitution, shall be eligible to the Office of President
or
(1B)
A Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President
and
(2)
Neither shall any Person be eligible to that Office who shall not have attained to the Age of thirty five Years, and been fourteen Years a Resident within the United States.