As a lawyer for over 20 years, I can tell you that a settlement that reportedly paid over $100,000 was not a victory for the Miss America contest. That is not what is called a “nuissance”* settlement offer. Certainly it was much less than the million that her lawyers reportedly first demanded. But that is not unusual that the lawyers would demand much more than they would really settle for.
I’d say that both sides realized that they had risks, and they both compromised. The revelation of the “sex tape” likely caused Ms. Prejean to lose stomach for the long hard fight that would follow if she did not settle. But if the Miss America contest had no exposure (no possible chance of losing) they would not have agreed to pay $100,000. That ain’t chump change.
* a nuissance offer is a small amount of money offered to entice the plaintiff to make a meritless law suit go away.