If we come across a customer who is running a money remittance business, but it appears that they are simply just an agent of a large company that facilitates those services, do we need to get the customer to register with FinCEN as an MSB, or do we simply need to confirm their agent status?

If for example you are referring to a business which is processing transactions for Western Union, the (small) business itself does not need to register independently as they are under the Western Union umbrella.

Confirm their agent status, i.e. ask for a copy of their agent agreement.