No, there's a huge difference between someone who is a citizen at and by birth, and someone who was NOT born a citizen of the United States but was naturalized at some point later in life.
Those who are citizens AT AND BY BIRTH (whether that status can be affected by laws set by Congress or not) is a natural born citizen. Those who aren't citizens AT AND BY BIRTH are not.
See my previous post. James Bayard wrote in 1834 that people in Cruz's situation were ELIGIBLE. And Chief Justice John Marshall, who of all persons ought to have been in a position to know, agreed.
At and by birth, or at and by statute? Cruz is a US citizen by naturalization statute.