This didn't seem right so I checked. A 20 year old in 1900 could expect to live to 62. In 1939 (4 years after SS was first put in place) a 20 year old would live to 67.
Interpretted as a median age of death, you are right that more than 50% of 20 year-olds collected at least 1 check, but a significant fraction died before retirement age, and they generally didn't say in retirement for decades.
http://www.infoplease.com/ipa/A0005140.html I used white males, and women lived longer but non-whites lived shorter.