HERE’S HOW TO UNDERSTAND IT.
In testimony before Congress about this very issue, many examples of the Privacy Act were shown. One of those examples is your right to vote. The State of Virginia tried to require the collection of social security numbers as a condition of voting eligibility.
The Court struck this down, because (now look back at the law):
It is unlawful for a State (i.e., Virginia, i.e., the government, i.e., not a private citizen or corporation, such as a bank) to deny any individual’s right (i.e., the right to vote) for such individual’s failure to provide his social security number.
NOT RELEVANT, BUT WORTH A MENTION.
We now know that the Privacy Act of 1974 only applies when the government is requesting your social security number. Even so, in some circumstances – which are not relevant here – the government can require that you provide them your social security number.