This was in 1938. Just three years after the Social Security Administration had been created. Most people still had telephone party lines. People didn't get how some government number could be really important.

You are thinking with a 2019 point of view, this was effectivly 1938, people were less aware of consequences of their actions (as history of that dark period shown accross the World ...). Also,probably at that time people thought that a real SSN would shine more than 000-00-0000, as any other number could potentially be a "real" number from an unkown person ...