A website visitor sent me this copy of an SS5 form completed in 1960. It contains a similarly worded stamp on the far left hand side. This card says "NO RECORD IN DAO"
This pretty much seals it for me. I don't think the Social Security Administration would use the word "DAD" on a stamp and they were concerned about tracking earnings, not anything else. Remember, this is the 1950s and 1960s we are talking about, not the 21st century.
