It's a good question and it gets to the heart of what many people misunderstand about what's going on in the system, and not just in this case.
Sorry for the long answer, but the answer is an area of legal theory, really, not just a factual question. (And it speaks to the unfair malign meant if lawyers as well!)
So let me try to distill an entIre jurisprudential theory complete with it's own literature and its application here into a single post...
Building off of DrL's "no" (which was accurate, but I think the non-legally engaged are looking for some more explanation) is that preference for settlements in civil proceedings are based on a very well developed theory of social utility backig this area of law. The idea is that to do litigation In a civil case, by the very fact of the costs of litigation, there is an "economic surplus" that can then be negotiated over such that settlement is in the best interest of both parties, even if one party is clearly "right."
Think of it like this: the thing being litigated over has some value X, which may be known ahead of time or may be yet to be determined, as by a jury or something. Either way, there is a value, X. But once suits are filed, it will cost a total of Y in litigation fees, opportunity costs, etc. to work out a resolution. That Y is, from a social utility standpoint, a deadweight cost paid to attorneys and is, theoretically, unnecessary. (Yes, even the courts and legal minds think this way.
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Given that cost of Y, there is theoretically almost always a settlement point that benefits both sides in that they get to share the division of that economic surplus, once you discount for the risk/probability of winning or losing. So the costs of litigation itself usually causes there to be a theoretically optimal settlement range.
Because settlement in this view is socially optimal--nobody wants extra money to just go to attorneys (seriously)--judges adopt a pro-settlement stance without prejudice towards the parties for a willingness to settle. And, as per above and from anything people have heard on talk radio, this makes sense and has nothing to do with pride or perceived guilt and innocence.
This is the generic theory, though, where all things convert into money easily. There are exceptions where it doesn't really scan, though, and this case is likely one of them. Brady may have a stake that cannot be compensated renumeratively, and Goodell may have reasons that make losing preferable to being seen as buckling and he doesn't personally suffer the consequences of losing.
But despite the irregular nature of the case, it makes sense for the judge to play it by the book with respect to the process of encouraging a settlement, even if the usual incentives may not apply here. There's even a term for the idea, "mechanical jurisprudence," which invokes the idea that the judge should just be cranking an impartial machine that does it's thing. He's not doing what he's doing for this case, he's just operating the machine--if you think about it, we probably don't want judges tailoring the process to what they think is going on sin cases on a case by case basis.
So yeah, with the caveat that people are human, a good judge won't be drawing adverse inferences from either side's position in negotiating, specifiscllY because
there are significant reasons for parties to settle independent of "guilt," "fault," "blame," etc. and, as such, such inference would be inappropriate.
Thank you for asking that, because this is an area where the public--and I know talk radio--has a tendency to run with some "common sense" notions that are fundamentally wrongheaded as compared to the very well thought out socially pragmatic approach adopted by our legal system. This case is a weird one, but the overall philosophy makes a lot of sense.