The obvious answer is that stuff happened that neither PSU nor Chambers wants to get out.Chambers resigned. What would he have to offer up to get an NDA? I'm just trying to understand why PSU would wish to keep it quiet if they were justified, and why Chambers would not want to address the smear job PSU already leveled against him. I will reiterate this scenario was posited by another poster.
Maybe it's embarrassing to both PSU and Chambers. Maybe it's something that Chambers did that would put PSU in a bad light if it came out that one of their coaches did it. Maybe it's something that Chambers did that he doesn't want to come out, and was willing to take less $ on the way out the door to bury it (and thus it helped PSU financially).
Any of those seem a lot more likely than a situation where PSU paid Chambers more than they needed to so that Chambers wouldn't talk, and thus hurt his chances of landing his next job if he did absolutely nothing wrong, while PSU wasted $ for no reason at all.