Here's the link to the Pacific Justice Institute's release on the case: "In his opinion, Croskey, 75, described what he called the "ruse of enrolling [children] in a private school and then letting them stay home and be taught by a non-credentialed parent."
http://www.pacificjustice.org/resources/news/focusdetails.cfm?ID=PR080305a
That's because the family never registered themselves as a private school, but tried to use Sunland Christian School as the supposed school ("enrolled" in Sunland Christian School). Since the children didn't actually attend the Sunland Christian School, and the parents never registered their own place as a school, the mother was not covered under either California Educational Code § 48222 ("Attendance in private school") for either place. Also, the court went through the other exemptions:
As I understand it and read the opinion, there's nothing that says there would have been a problem if the mother had registered the home as a private school, like tens of thousands of other homeschoolers do.
Should that red tape paperwork bureaucracy be required? Maybe not. But it's the current law and compared with many registrations, it doesn't seem horribly onerous.
If they want to get the law changed so registration isn't required, then they should do so...but as it stands, the requirement is to register the homeschool as a legal "private school"--which is defined by these requirements: