You apparently have a narrow view of what civil litigation is about. In many of the cases I handle, there is a lot of discussion and negotiation prior to any lawsuit being filed and yes, quite often offers are made in that process even before a complaint is filed in court. Indeed, a lot of matters can be settled without the need to go to court at all. 

I have no idea what the right position is for the OP to take in his/her particular case because I don't have anything close to all the facts needed to make that assessment.For that, he needs to consult a lawyer in his state that handles copyright litigation matters.