It is interesting that they would say they need an affidavit from a judge. Ordinarily, if an estate is worth $150,000 or less, life insurance, retirement benefits, and the like can be transferred by affidavit signed by a notary. The court's self help center may have a guide or form for you for this, but if not the California self help site does as well, and I have provided the web address below. It is a great place to begin, especially if you are not familiar with how the estate transfer process works in California.
Now, if the amount is in excess of $150,000, then a Petition for Probate - or, more specifically, a Petition for Letters of Administration, as there is no will, may have to be filed. This is also discussed in detail on the above site and forms can be found there. The administrator, appointed by the court, acts as a sort of personal representative of the estate to collect the deceased person's assets, which would include benefits such as those you describe, and distributes them to the heirs.
The probate process is quite complicated and more costly compared to the affidavit process, and what the insurance
company told you doesn't really make sense in the context of California law. With that being the case, it might be a good idea to contact the insurer to get something in writing that explains what they are asking for and then take it to a local wills and estate attorney who can review the paperwork and help you decide which process will be required. You would also be better able to determine whether you would prefer to handle it all on your own or retain the attorney for full representation
. Though the site above provides detailed instructions a to how to proceed, it can still be a complicated process when substantial amounts of money are at issue, and so it is generally recommended that an attorney be retained to assist when probate is required.