I don't think this is true. Average life expectancy in 1933 was 61.7 for men and 65.1 for women. But that includes childhood mortality. One infant dying has more effect on that number than someone living into his 70s. I would like to see a figure on life expectancy of those who reach 18. That would show how viable Social Security was.
My father's generation was the first one where you expected all of the family's children to live to adulthood. My grandfather lost at least two siblings.
My father’s parents died in their fifties.
My mother’s father lived to age 74 and her mother lived to age 72.
My Uncle Tom is still going strong at age 99.