Those quotes are the Secretary of State's interpretation of the laws, as far as I can tell and not the wording of the law itself.

https://codes.findlaw.com/ca/elections-code/elec-sect-11381.html

"No person whose recall is being sought may be a candidate to succeed himself or herself at a recall election nor to succeed any other member of the same governing board whose recall is being sought at the same election." This precludes being an official candidate, but the election law elsewhere makes it clear that official candidates and write-in categories are different categories of individuals, and the law does not explicitly forbid a write-in candidate.

Similarly, the Secretary of State's interpretation of what constitutes a legitimate write-in candidate may not hold up in court. Her interpretation of what tax forms needed to be submitted by official candidates did not hold up.