Actually that's not completely true, not now anyway. If your parents are both US citizens you are automatically assumed to have American citizenship up until the age of 18, wherein you decide your citizenship based on two factors. If by the age of 18 you live within US borders, you are then American. If you still live outside US borders but register to vote in the US, you are then granted American citizenship.
If you have parents with two seperate citizenships and are born inside US borders {ie one American parent and say One Canadian parent} your dual citizenship is recognized until you register to vote or move outside US borders.
My father is Canadian, my mother American. I was born in the US, but until I was 18 we claimed dual citizenship when crossing borders to visit family in Canada, as well as on our return to the US.
As soon as my brother and I turned 18 and registered to vote, we lost our Canadian citizenship, as far as the US was concerned. But in Canada, we retained dual citizenship. I know this because even after the age of 18 and having registered to vote in the US, Canada still recognized my dual citizenship when I was visiting my Canandian family and needed medical attention. Because I retained my dual citizenship, Canada's national healthcare system allowed me access to healthcare as needed.
To this day I can still obtain healthcare from Canada if I'm ever up there.