Not true. My cousin is an American Born woman who is married to an Eastern European and they live in France where he is employed as a lawyer. They met in the US. Her children are not natural born Americans. They are also not French citizens. They do carry both American and Estonian passports. At the age of 18 with the use of the passports and ticket stubs showing a total time spent in the US of 4 years they can declare their American citizenship. If they want French citizenship they have to apply for it at age 18. If they marry an American, then any children born to them in the future would be American but have to be born in the US to be Natural Born. If they marry a Frenchman or any other nationality, the 4 year requirement must be met for them to claim American citizenship for themselves. It is complicated according to my cousin. She should know, she has been in France now for about 10 years and has 4 kids.
According to law, yes they are:
"The following shall be nationals and citizens of the United States at birth:
g) a person born outside the geographical limits of the United States and its outlying possessions of parents one of whom is an alien, and the other a citizen of the United States who, prior to the birth of such person, was physically present in the United States or its outlying possessions for a period or periods totaling not less than five years, at least two of which were after attaining the age of fourteen years...
Unless she hasn't lived in the U.S. for more than 5 years of her life or if two of those years weren't after she reached 14 then her kids are natural born U.S. citizens.