No person shall operate a meat processing establishment unless all livestock and poultry products used in processing and to be sold have been inspected by the United States Department of Agriculture, fallow deer products have been inspected at a custom livestock slaughterhouse, or poultry products have been inspected in accordance with the requirements of Chapter 3 (commencing with Section 24951) of Part 1 of Division 12 and the processing of the product is inspected by a licensed processing inspector.