So you'd want some robust supplier quality assurance but also some testing if you can (and have the money) or sign up to one of the food fraud intelligence networks so you can be alerted and can grill your suppliers on emerging issues.
For a 3PL our "suppliers" are our customers who would heavily frown on us opening their packaging and testing it. Especially as many things are proprietary and they still own the product.
We get product in and store it until our customers tell us where to send it. Most of it stays on the same pallet it comes in on, and occasionally we will "pick" pallets by adding a variety of that customers products onto one pallet. Most of our product is finished product that is ready for store shelves. Some is raw ingredients that we store as overflow for certain customers or until they have a customer we can ship it to on their behalf. We (most 3PL's) own zero product stored in our warehouses.
Cheaper fish and horse meat would not be something we could catch as we don't touch any actual product unless we are tossing it due to damage. If we see exposed product, it is damaged, otherwise we can only go with what the label says.
FDA says we are exempt from a food fraud mitigation plan, but it's still in the BRC and SQF Storage and Distribution code so we are left weeding through everything that is designed for product before it's in it's final packaging. It's a frustrating journey.
It's exhausting trying to take programs that are meant for certain specific functions (HACCP and SQF as a whole) and fit my little part of it into a plan that will get us certification and not kill my warehouse staff. I've only been doing this for 7 months when our other warehouse (8 years at a hazmat facility) closed and I've made a lot of changes (my company is over 100 years old and we have people who have been with the company 40+ years) and I keep getting asked why on a lot of little seemingly crazy changes we've been implementing. Does a storage and distribution facility with no exposed food REALLY need to sanitize their brooms and dustpans??? AND have different colors for allergens and glass (in a facility that hasn't had any glass breakage in years)?? You want me to count the windows and light bulbs? Can we really not tape something on our lift to hold pens and labels? Why can't I prop open this door and go talk to the driver? I see the hole, but it's not actively leaking, so why can't it sit there until someone else sees it and decides to do something about it? What, you want me to actually put this bag of leaking rice in another bag so it stops leaking??? Why haven't seen a rat in the building for 20 years!