Re: Australia versus New Zealand
Do you realize that there are people who live here absolutely legally for years, but don't have a SSN? So, according to you, they won't be able a get a police clearance certificate? I don't think so.
In fact, here is the reference to the Office of the Attorney General's website and there is nothing about providing a SSN there.
http://ag.ca.gov/fingerprints/visaimmigration.php
There is a field for a SSN in the application, but it does not says it's mandatory. The same is for the DL. Simply because people may not have them. Period.
In fact, the only mandatory fields are listed in the
Instructions for Visa/Immigration Request Form and they are:
Type of Application, Reason for Application, Name of Applicant & Personal Descriptors - "
Name, date of birth, and sex are mandatory fields and must be provided. All others are optional" Applicant Address, Daytime Telephone Number.
http://ag.ca.gov/fingerprints/forms/...ation_info.pdf 
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