Not true.
According to citizenship law in effect at the time of his birth, she was not old enough to automatically confer citizenship to her son at birth.
But it only applies to an outside the country birth. It's not so much she wasn't old enough, but rather she had not lived in the US long enough after her 14th birthday. Same thing almost, but someone could be 25 and still not meet the residency requirement if they had lived overseas most of the time after turning 14.
The requirement also only applies if the US citizen parent is married to an alien. It's much less if both parents are citizens or the mother is not married.