For folks not in the know, "NDA" is "nondisclosure agreement". When you hear that a "confidential settlement" was achieved, an NDA was signed. That means, break it, and the settlement is void (and you have to give the money back). Totally unrelated, but, near the end of the movie "Spy Game", there is a scene about signing the NDA.
What irks me is that the OP is, presumably, new to these new, miserable experiences. As such, s/he is being bullied - as if his/her program is being SO magnanimous, that they would "let" him/her go with the NDA, when the OP is 100% in the right. In reality, they KNOW they are wrong, but they are, in fact, bullying the OP into accepting it. However, since the OP is "green" at this, s/he doesn't know how strong is his/her position. It is unfortunate that the OP didn't have a strong orator in his/her corner, such as an attorney, to be honest, someone like me, who would have leveled the playing field. It's confusing to be told you're wrong, when YOU are the one wronged.
This long screed is just my opinion. However, if the OP can just "get the hell out of Dodge", I'll count that as a "win".