The CRA has a statutory requirement under FCRA 611(a)(2))A) as follows:
"Before the expiration of the five business-day period beginning on the date on which a consumer reporting agency receives notice of a dispute from any consumer or reseller in accordance with paragraph (1), the agency shall provide a notification of the dispute to any person who provided any item of information in dispute, at the address and in the manner established with the person. The notice shall include all relevant information regarding the dispute that the agency has received from the consumer or reseller."
There is no question that, even if the CRA conducts its own reinvestigation from other soureces, they are still required to send notice of the dispute along with all relevant information that you provide to any party who has reported any information covered under the dispute.
An MOV request under section 611(a)(6)(B)(iii) must provide, at a minimum, a showing that they communicated your dispute and supporting information to the party who reported the disputed information. They must provide a descprition of the procedure used to make their determination.
Additionaly, under section 623(b)(2), the furnisher of the disputed information is then under a required statutory period to respond back to the CRA prior to the expiration of the CRAs reinvestigation period So the issue of receipt of the statutority required response from the furnisher is also, in my opinion, part of the 'procedure used to determine the accuracy and completeness of the information,' and thus to a legitimate part of your MOV request.
I would argue that a response to any MOV request that fails to disclose forwarding relevant information regarding your dispute is a prima facie violation of section 611(a)(6)(B)(iii), and thus would be grounds for holding them in lack of compliance with the required reinvestigation of your dispute.