And IIRC, NO ONE can force you to give your SSN (other than, of course, government entities ... and even then, they have restrictions on WHEN and HOW they can demand it).
Several "Acts" (such as the HEA, The Debt Collection Improvement Act, etc, had to be enacted in order to allow various government bodies to collect your SSN info legally.
Sooo ... if the Feds need special permission to demand your SSN, what makes that CA think they have a right to it?