If they responded to the DV with verification, they have stated that they have investigated the debt, and have reasonable basis for asserting a continued debt.
Waiting it out will, once 7 yrs plus 180 days has expired from the DOFD on the OC account, exclude the collection from your credit report, and thus prevent others from becoming aware of the unpaid, delinquent debt by seeing an active collection on the debt.
However the debt remains unsatisfied, and if potential creditors become aware of it by other means, it can remain as a basis for denial of future credit.
While you may assert that the debt does not exist, they have verified that it does. It can still come back to bite you.
A seetlement for as low an amount as possible would satisfy the debt, and remove that lingering issue.
When you are applying for a mortgage you have to disclose unpaid debt. Even some employeers ask this also.
If you apply for a mortgage or credit of $150,000 or more or a job with an annual salary of $75,000 or more they can get a report that shows all unpaid debt. It is rare but it can happen.
Unpaid debt does not go away.
Also, they are not required to prove you own the debt, just that one exists. It would be up to a judge to have them prove that.