According to FDCPA, arent they required to prove that this account is mine? Like a signature, ID copy or something, proving that i availed the services?
For purposes of doing collection, they are required to provide only very little under the guise of validation. That could change in court if they sued you for the debt or if you sued them for incorrect credit report entries they refused to remove.
Send them a cease and desist letter and they are required to stop communicating with you unless they want to sue (and then they have to do only the formal communications of a lawsuit, and only with your attorney if you hire one).