From my experience, those people will tell you anything if they think they can intimidate you into paying. They buy charged off accounts from credit card companies in hopes of reaping $$, though it will not improve your credit report.
Maybe next time you could ask them to hold while you press the “record” button, or even perhaps a call back number (direct to the agent calling) so that your lawyer can call them to “negotiate.” I’d bet they’d leave you alone for a long time.
You need to read up on the Fair Credit Act (or some such). I believe that before they can do anything they must write you their reasons and their requirements (requests) of you and then you must be given something like 30-90 days to respond/contest it.