Walmart is making this change to improve something. They obviously already have a database somewhere with suppliers and shipments and to think they don't is just crazy.
Sure, contract law. But why when there is a technical solution? If there is a dispute that then has to be settled in the courts with your solution that costs more money and time. The 6 days to 2 minutes might end up way longer after amortizing time spent dealing with trails and compliance and ensuring suppliers are doing things right.
I think I don't see any of the multiple trust relations solved in this case.
Walmart still can't trust the producer to itemize the physical product correctly.
The producer still can't trust Walmart to not change the item already in the database (see mining discussion above).
What trust relation do you have in mind, that is solved with this blockchain implementation, and that wouldn't be solved with a ordinary database with signed entries?
As Walmart is the sole owner of the database anyway, nothing is gained by using a blockchain.