California law makes it very clear to funeral homes exactly who has the authority to sign off on the cremation or burial process. The person or people whose signatures are required is laid out in Health & Safety Code 7100, and we are not allowed to deviate from this list.
Roughly, the list starts with the Durable Power of Attorney for Healthcare (if the decedent had appointed one) and moves down through the spouse, adult children, parents, adult siblings, and so on.  Where it can become complicated is when there is more than one person in a group, ex. more than one child, or multiple siblings.  In that case, the law is clear that the "majority" of signatures is required. Seeking signatures from multiple children and siblings can add time to the process, but it is necessary for the funeral home to keep everything above board.