To answer your question, the permissioned networks already have a consensus mechanism that will require permission to join and participate. Hence, using a blockchain adds little or no value to the operation of the system, other than a mechanism to verify data integrity which you've rightly pointed out, could already be done easily before blockchain was created. But however, using a chain of blocks is not the innovation, the innovation is joining it with the proof-of-work to achieve consensus in a distributed, public and trustless network.