When you dispute, the CRA is required to forward a copy of the dispute to the furnisher, and the furnisher is required to conduct a reasonable investigation of their records, reach a determination as to whether their reporting was accurate, and convey that determination back to the CRA.
The furnisher is not required to document or prove their determination/verification of accuracy.
If the issue is one of asserting the debt is not yours, that usually wont wash. The creditor will have some type of documentation to support their finding, and thus can legitimately verify. To get a full hearing of contested facts requires bringing civil action, and getting all the facts before a judge.
That is the reason for the prior suggestion that the alternate remedy is to assert, in a sworn police report, that you never authorized the account or transaction, and thus its reporting was due to improper use of your identity. A sworn police report enables you to invoke the identity theft provision of FCRA 605B, which requires the CRA to block the reporting from your credit report is backed by a sworn police report. That process avoids proofs over who is right or wrong, and at least gets the reporting blocked from your credit report.
As for resolution of the dispute, the CRA is required to complete their reinvestigation within 30 days, and send you a formal Notice of Results of Reinvestigation within 5 days thereafter. That Notice must clearly inform you of the resolution of the dispute, and if any information is update, amended, or deleted as a result of the disptue, must provide you a copy of your revised credit report showing that the changes have been made. Their should be no ambiguity if any change was made.
I dont thhink their leter was their formal Notice of Results of Reinvestigation..