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No.
The FCRA requires a furnisher to conduct a reasonable investigation and respond back to the CRA that referred them the dispute.
That response must be provided within the CRA reinvestigation period. A furnisher cannot alter a statutory requirement by way of an agreement with the consumer.
If you file a dispute, you are contesting the accuracy of their reporting. They must investigate and respond back to the CRA.
Additionally, if any previously reported information later changes, they are also required under FCRA 623(a)(2) to update that reporting so as to reflect its current accuracy.
Agreement not to update applies only to voluntary updates that are not otherwise required by statute or regulation.