Not exactly, a contract must bind both parties to do something. You cant have a contract which states "you give me money and you dont say anything about it." It must also bond the other side: "and in return I will not sue you for piracy committed on the date of..."
You missed chacham's point. You are right that both parties have to agree to make a contract. But on top of that it's not a contract unless both sides get something out of the deal. If you sign a piece of paper to exchange $10 for nothing, it's not a contract.
The idea being that for "normal" people, doing anything through the civil justice system is far too expensive and time consuming than just paying out up front.
So the choice is simply: Pay X up front and promise not to tell anyone, then be left alone
OR
Don't pay, attempt to fight it in court (using lawyers/solicitors/barristers) and absorbing the cost of this upfront yourself, regardless of the outcome.
If you or I tried to do this, we'd be sued into oblivion for blackmail because that's what this is, blackmail. Pay us money and we won't tell on you. This world is messed up.
There have been more egregious examples of this with regards to piracy of pornography.
A few of the accused tend to stand up (grandparents who don't even own a computer, etc.) but I bet most just pay up to avoid the embarrassment of being dragged through the courts accused of pirating some smut.
Courts are best as you can put in counter claims and with todays technlology we still don't have storage that ties up that data to a user that is as good as DNA and DNA is not perfect.
Counter sue, entrapment, backmail, bullying, cartell - just anything remotely tangable then chuck it at them back. There rules after all
Seems pretty creepy.