Is it legal for Direct Recovery Associates to threaten credit damage over an old debt?

Direct Recovery Associates has been pursuing me for a debt that I believe is past the statute of limitations. In their latest letter, they strongly implied they would report it to the credit bureaus, which has me worried. I'm not sure what they can actually do. While researching, I came across some information on how to handle collection harassment that might be helpful. Has anyone successfully dealt with them over an outdated debt? Any guidance would be appreciated.