This is not true. I was born in Canada to an American-citizen mother. I had to go through the naturalization process. I was NOT considered American-born.
If I remember my history lessons, I believe there are two laws in play with regard to citizenship:
1. The Law of the Blood - You are a citizen of the country your parents are a citizen of; and
2. The Law of the Soil - You are a citizen of the country you were born in.
If you were born in Canada to an American parent, you have dual citizenship. It is beneficial that you declare citizenship to one country, but not required.