Perhaps not quite all. The 14th amendment declares that all persons born in the US and subject to their jurisdiction are citizens. That category is likely not quite congruent with "natural born citizens".
It is unfortunate that the authors of the 14th could not have been a little less ambiguous. While they were clear enough as to what they meant at the time, and tried to say it with economical language to ensure that the descendants of slaves were not denied their citizenship, the wrongly decided and horribly reasoned Wong Kim Ark case has perverted and altered the intended meaning of the 14th, and as a result, today we have a continuing Constitutional miscarriage that would have horrified the legislators who drafted the 14th:
Anchor Babies.