A blockchain is a ledger, perhaps a better way to manage a ledger. An open, permissionless blockchain has the great features of being decentralized with a distributed network of miners providing the muscle to process transactions.
Miners' main goal isn't verifying transactions, they simply put timestamp on it. If you run a small private network, you don't need mining. As for open and permissionless ledger, why would companies need it?
Should it be a new, proprietary blockchain just for this customer, or an existing blockchain? Could a blockchain like this piggyback on an existing coin? Could Ethereum be used store, verify and process a company's general ledger transactions? Would this be a cheaper, more secure way to do it? Would this beat the cost of using a traditional ERP system with a local database maintained by the company?
If a company wants to store some data in publicly available database that can not be changed, then using existing blockchain, like Ethereum, is an ideal solution, because creating a new blockchain just for their need is never going to work.