The legal obligation to delete information from one's credit file is triggered only if the consumer has disputed, and in the resolution of that dispute, the furnisher of the information either confirms that the reported information is inaccurate, or they do not state that they have verified its accuracy. FCRA 623(b)(1)(E). They have 30-days from the date of dispute to provide the verification back to the CRA.
It does not appear, at this point, that you have a notice of dispute resolution that confirms, as a result of their reinvestigation, that the information has not been verified. To the contrary, you have a dispute that has been verified as to accuracy.
The CRAs wont, and shouldnt, interject themselves into the issue of creditor verification.
You must first have a dispute resolution that evidences lack of furnisher verification before you can compel the CRA to exercise the deletion of the disputed information.
Having once filed a dispute that resulted in verification, the CRA can simply dismiss any subsequent dispute that contains no new documentation as being duplicative, and thus being "frivolous or irrelevant."
Maybe you can assert that the current representation that they have no records upon which to verify the information constitues "substantially new information" that would justify a renewed dispute. That would be my suggested route. And use of the direct dispute process rather than through the CRA would remove any CRA meddling in the issue, and thus prevent them from refusing to even forward the dispute to ther reporting party.