it is based on each state's collection laws, but most states have that "oral agreements" constitute a renewed statute of limitations (not the Fair Credit reporting Act)
of course, debt collectors have to record and save your conversation of your oral agreement to furtherance of the debt and its statute of limitations--some keep an entire library of such conversations. But I would insist in everything in writing from now on...of if beyond the statute of limitations, draft a "cease and desist" letter.