For fighting for the same money you or I would fight for if put in the same circumstances.
Under same circumstances (your phrase, respectfully offered by someone who agrees with you way way more than not), I'd settle . . . and I think you would too.
I also wouldn't expect, under the circumstances, for the other party to just say, "Oh, OK, here" . . . and I don't think you would either.
If, "Nah, you get nothing," was the University's opening gambit, then I'm completely on board with you. It would be pretty irregular and strategically foolish if they in fact did that
If an offered settlement was insultingly low, then I'm still along for the ride, but I'd want to know more about counteroffers and posturing.
All of that said, I don't know what was or wasn't offered, or what was or wasn't countered. Do you?
I haven't seen anything reliable here that suggest anyone posting knows.
That would be the basis for my casting a skeptical eye toward some of the hardline positions taken here.