I believe what was missing in your documents is "the method" that the assistant manger is using to approve the materials. Below it what the auditor will be looking for (extract from the guidance doc. SQF S&D Mod 2, top of page 23)
"The auditor will seek evidence of the existence and currency of product descriptions and a procedure for developing and approving them at the desk audit. During the first and subsequent site audits, the auditor will confirm compliance to this procedure and the process for checking compliance and validation. Evidence will be sought by interview, review of descriptions and record review, and may include: • Review of the procedure for developing and approving product descriptions; • Confirmation that the list of products used in the facility matches what is inventoried; • Review of a selected sample of products to confirm agreement with relevant legislation; • Availability of current copies of descriptions to relevant staff; • Interview of staff using the products and those conducting validation activities;"
You can add to your 2.3.2 document that the assistant manager will run a procedure that will consist in ensure the product is approved to be use in a food warehouse, for example. There you list your procedure and what will determine if the product is "approved".
Remember here the code is referring to "all incoming supplies used by the site but not intended for distribution".