If you don't think you owned the debt, and the creditor cannot verify, then you don't owe them. Validating debt is one of the tools used in negotiating creditors. It's forcing them to check that the debt is yours by demonstrating where the debt originated from and the amount. Ultimately a letter must tell the debtor who owns the debt; the collection agency or the original creditor.
The Fair Debt and Collection Practices Act has specific language dealing with these types of situations. When the collector fails to verify debt, the debtor needs to send out a letter informing them that they are disputing the debt. All collection activities on the part of the collector has to stop and any reports to a credit rating bureau must be lifted. Attempts can resume if they manage to somehow find proof of the debt.
Do not make any payments to the agency as you're admitting liability for something you don't owe. Doing so will only make life worse for yourself. Be patient and wait out the collector. If no evidence of debt exists, they will have to leave you alone for good.
Retaining a lawyer for these types of situations is the best line of defense. A collection agency is less likely to make trouble over this type of situation when they have to talk to a lawyer. They're aware that the act of hiring a lawyer means that the supposed debtor is more than willing to take legal action against them.