Wrong. You can send them a do-not-contact letter. If they call you after that, they me liable for $1,000.00. They may sue you, but unlikely if you don't owe the debt. If they do, you'll win as they won't be able to prove it.
I did a little research on the internet. What I have found applies only to the state of Missouri, but I would advise that local statute of limitations be checked.
The statute of limits for open accounts (credit cards) is five years (Section 516.120), and written contracts are 10 years depending on the circumstances (Section 516.110).
http://www.bills.com/blog/missouri-collection-laws/