I can definately see your point, but that incident starts earlier. With his bad choice to date this woman, the woman's possible choice to see another man at the time they were in a relationship. I mean there's nothing definite that she cheated on him, just his claim not to be the father...paternity tests during pregnancy are forbidden in Germany for example, don't know about the USA. I agree that's a lot of pressure that's applied on that woman, but I the way I see it she's very responsible to let a situation escalate like that.
If I were Reddick I would have rather tried to negotiate for terms that say, he's not responsible for the custody of the child, no matter what she decides to do with it and connected that with a payment that forbids her to talk to others and the media about their relationship and pregnancy. This would preserve his public reputation and at the same time prevents her from collecting money from Redick.
Then the responsibility would be all with her. Plus this situation doesn't prevent him to financially support(for example by letting thirds send money) the kid if he looks like him clearly as an visual confirmation of his paternity.
The choice of words in that agreement is very harsh and all indication of what kind of whore that woman is leads me to the conclusion that she'd pursue the case/blackmail him further if there wasn't reasonable doubt about his paternity. I'd be way more intersted to see what the "more likely" father has to say to the topic.