There are hundreds of thousands of living Americans older than the SSA! Think about all the people that never had birth certificates because they were born at home or in a poor rural hospital, or the side of a road, etc. My sister's "official" birth certificate is a letter from the US embassy (in a country that no longer exists), telling the state department of the birth of a US citizen abroad, to an active duty serviceman.
Real data is messy, and theirs is especially so.