This is the main value of a blockchain. You can do business with someone you don't specifically trust without requiring a third party in the middle to mediate the financial transaction.

The only people that need to run a verifier node are those that don't trust the other verifier nodes to do it properly. It's opt in, most will not run one, but a business that has enough money at stake can if they want to.

Then the blockchain client software provides the framework for cryptographic assurance that the two copies of the ledger are in sync.