My take on your situation is this. Of course they will let you settle on behalf of the site owner. That means they win. It also means they can hold out for a little more because their fallback position is to go after the site owner. They will not approach you because even though you consider yourself responsible, the law only lets them go after the site owner. (Note, I am not a lawyer).
A corollary is that once you come out and let them know that you have a conscience and want to make this right for the site owner, they know they have their hooks into you. My suggestion is that if you do contact them, expect to ante up something close to their asking price to settle. If you can make them believe that the site owner hired Oscar and the letter program, I'm pretty sure they can no longer contact the site owner, which should take some pressure off of you.
Lastly, there is a lot of good information on these forums. Everything I know about this process, I learned here through first hand experience. Don't underestimate the value this site can be to you. Put your time in to get educated before embarking on a course of action.