Legal Question in Civil Litigation in California

You misunderstand the purpose of the Government Code claim process. It has nothing to do with secrecy, publicity, or privacy. It exists to allow government entities to settle legitimate claims without litigation, particularly since once a lawsuit is filed the court costs and sometimes attorneys fees are added to the claim. If a claimant has a legitimate claim, the public has the right to have their government settle that claim instead of wasting tax money on lawyers and costs. Furthermore the claim forms are public records, accessible to anyone who makes a public records request. So the Government Code claims really have NOTHING to do with avoiding publicity.

The other things you mention, publishing social security numbers and stating the amount of punitive damages sought, are prohibited, not to prevent publicity either, but rather for other public policy reasons. The rule on SSN's is obviously to protect people from identity theft. The rule on punitive damages is two-fold. First it is to focus the litigation on the real damages, and not get the plaintiff betting on the court delivering a lottery payout in the form of punitive damages. It keeps the litigation real in order to foster settlement. The second reason is that the complaint is sometimes read to, or read by the jury, but the jury is not supposed to contemplate punitive damages unless and until there is a verdict awarding punitive damages in general. If that happens then there is an additional trial proceeding to determine the amount. The courts don't want juries prematurely considering the amount of punitive damages. Again, nothing to do with publicity.

Government claim forms are most likely not considered private or privileged. However, some of the information one puts in a claim form might be considered private. Before taking such action, you should probably have the form reviewed by a local attorney for your own protection.