I'm not sure why the big surprise here. As the quasi-official historians of the US scheme would tell you, they copied Bismarck, just some 40 something years later (and more or less for the same reasons):
Thus, the United States embarked in 1935 on the road to providing its working population with old-age pensions, following in many respects the social insurance models adopted by Germany in 1889, Belgium in 1900, the Netherlands in 1901, Austria in 1906, France in 1910, Italy and Spain in 1919, and Hungary in 1928 (Social Security Administration 2008).
[...] At their inception, most European old-age insurance programs covered only blue-collar workers, reflecting their governments' desire for more stability in the labor markets and to fend off the political threat of national socialism and communism.
Even the noncontributory, means-tested flat-rate pension adopted by the United Kingdom in 1908 seems not to have elicited much enthusiasm on this side of the Atlantic, although the United Kingdom was the leading industrial power of its time and its historic ties with the United States would have meant that American experts closely followed British social security developments. There was a similar lack of enthusiasm regarding the Canadian initiative, which put in place a universal federal old-age assistance program in 1927, and left the United States as the only major industrialized country which had not implemented a public old-age income security program before the Great Depression.
[...] It is not surprising that the U.S. reformers felt generally more comfortable with the Bismarckian or German model of social security protection (mandatory social insurance financed from payroll taxes) than with the UK or Nordic approach of universal benefits (often flat-rate benefits subject to a means or earnings test). The consensus from President Roosevelt down to the original members of the Committee on Economic Security was that Social Security should not be compared to the "dole." In arguing for Social Security, Roosevelt clearly made the distinction between social insurance and social assistance, drawing on the American tradition of individual responsibility and self-reliance as being more consistent with the social insurance approach.
If you insure your house and it burns down you can get paid more than what you've contributed to that date. In order for the overall program (or insurance company) not to end up broke, some people will collect less than what they've paid in.
This is also admitted in that quasi-official history, albeit with a bit of sugar coating:
Although Congress has commissioned numerous studies, and public interest groups have invested enormous amounts of energy into finding a solution, the twin goals of the Social Security program—social adequacy and individual equity—remain in occasional opposition.
By the time America adopted its first national social insurance plan in 1935, there were already more than 20 nations around the world with operating social insurance systems (Liu 2001). The first Social Security retirement system was put in place in Germany in 1889. [...]
Because social insurance began in Europe decades before it crossed the Atlantic to our shores, there was time for the development of American expertise on the subject. Among the notable academic experts were Henry Seager, professor at Columbia University, who authored the first American book on social insurance, and Barbara Armstrong, professor at the University of California at Los Angeles (Seager 1910; Armstrong 1932). Two social insurance advocates stand out: Isaac Rubinow and Abraham Epstein (Rubinow 1913 and 1934; A. Epstein 1936; P. Epstein 2006). In addition to these advocates for a European style social insurance system, there were related developments at the state level in America before 1935. [...]
This extreme economic climate of the 1930s saw a proliferation of "pension movements," most of which were dubious and almost certainly unworkable. The most well known of these radical pension movements was the Townsend Plan. It promised every American aged 60 or older a retirement benefit of $200 per month—at a time when the average income of working Americans was about $100 a month (Amenta 2006). Huey Long, senator from Louisiana, offered his Share the Wealth plan; Father Charles Coughlin, the radio priest, advanced his Union for Social Justice; and the novelist Upton Sinclair promoted the End Poverty in California plan. Millions of desperate seniors joined efforts to make these schemes national policy. As the clamor for old-age pensions rose, President Roosevelt decided that the government needed to come forward with some realistic and workable form of old-age pension.
BTW, if you wonder why the first bit mentioned national socialism (which wasn't yet a thing as such in Bismarck's time), it's probably in part because of Coughlin was a thing during the FDR years (although Coughlin's positions were more like clerical fascism, but with a strong economic populism component, which he melded with some anti-semitism, often couched as anti-[international-]bankerism etc.)
Roosevelt himself seems to have seen the Townsend Plan as a more concrete political threat though, at least in that narrow regard (Wikipedia):
By January 1935 there were 3000 clubs nationwide with 500,000 members. They circulated petitions to Congress with 20 million names. [...]
Frances Perkins, President Roosevelt's Secretary of Labor, in her memoir, The Roosevelt I Knew (p. 294) says that Roosevelt told her, "We have to have it [Social Security]. Congress can't stand the pressure of the Townsend Plan unless we have a real old-age insurance system."
So, yeah, the Social Security as adopted back then was a somewhat moderate solution compared to some alternatives that were being aired.
And if someone is curious how Rubinow argued this old-age issue, here's an excerpt from his 1904 article:
Permanent disability, moreover, may happen from other causes
than accidental injury, as from invalidity due to sickness, or from
As saving, on the one hand, and charity, on the other, are the
ordinary methods of meeting the failing power of production in
old age, so old-age insurance may be made to approach either
saving or public help. Where old-age insurance is made to depend
upon the individual contributions of the workingmen, it is, after
all, only a modified form of saving. If society is made a partial
or chief or sole contributor, old-age insurance is nothing but a
guaranteed form of old-age pension. From a sociological point
of view, the workingman who has spent his life in socially useful
and necessary toil is entitled to support during his old age-entitled to it not as a matter of public safety, the basis of most of
the charitable work done today, but as a matter of justice and
right. Here is the difference between the English poor-law and
a system of old-age pensions or insurance. If, however, a small
individual payment from the insured be required, it may have the
value of giving the insured the illusion that in getting the pension
he is not exactly a public charge. But this psychological value is
only temporary and conditioned by the laborer's lack of education.
A soldier is not ashamed of his pension. Why should a workingman be? Are we ready to admit that a life full of toil is of less
social value than a life full of play and parade, with a few occasional battles thrown in?