I think it would depend on if you outsource your bill payment functions or process transactions in-house.
We have an Internet Service Provider that outsources the bill payment function to another vendor. The ISP has the responsibility of performing vendor assessments.
Since the processing agent initiates the ACH credits, and the credits may be sent via check, electronic transmissions, or ACH to the vendor payees, I would think it is the vendor's responsibility to perform the check.
In some outsourcing instances, the FI might not even know who the payee is.