Advantages of a Permissioned Blockchain
Companies are turning to private permissioned blockchain such as Hyperledger Fabric (The Dutchess Project) to solve different problems that arise in systems dealing with trust. For example, in systems dealing with consent or approvals, the signing mechanisms give a simple mechanism to see whether parties have signed off on a transaction.
Take a shipping system delivering to multiple locations. If a delivery were marked complete when 3 boxes arrived at different locations, only one of which I am present at. If each of the locations had a hyperledger user present on the channel, I could deploy chaincode on the channel to update a delivery as fully complete if and only if all 3 users verified that the object was received. Then, each user can check for the status of the delivery on-chain to see that all 3 other parties have checked off on the delivery. This could be further expanded by adding time or other requirements, to tailor the acceptance criteria to fit a use case.
While a single database accessible to all parties may accomplish the same thing, this allows all 3 parties involved to maintain a copy of the record and independently verify the integrity of the ledger.