The short answer is “no.” California Government Code Section 935.4 allows School Districts to designate an official to handle claims for itself as long as those claims are not over $50,000.00 in compromise or settlement. Now, that does not mean that a School Board cannot decide to put in a lower threshold and be more active in the claims process. And yes, I am aware that the text actually seems to read in reverse.
935.4. A charter provision, or a local public entity by ordinance or resolution, may authorize an employee of the local public entity to perform those functions of the governing body of the public entity under this part that are prescribed by the local public entity, but only a charter provision may authorize that employee to allow, compromise, or settle a claim against the local public entity if the amount to be paid pursuant to the allowance, compromise or settlement exceeds fifty thousand dollars $50,000. A charter provision, ordinance, or resolution may provide that, upon the written order of that employee, the auditor or other fiscal officer of the local public entity shall cause a warrant to be issued upon the treasury of the local public entity in the amount for which a claim has been allowed, compromised, or settled.