No, this was not by any means a "great article on the legal Xs and Os". It was a one-sided article giving voice to a guy who was putting the (legal) case for the NFL.
It goes in two steps.
1. Kurlantzick sustains the Article 46 ("conduct detrimental") claim. Kessler has been trying to argue that Article 46 isn't applicable and such articles as Chatham's seek to back it up. This guy argues that there are important differences between this case and, say, the Petersen case. Ones that are significant enough to make Article 46 applicable. (Sorry, Mr Grid!)
2. He then argues that the courts must defer to the arbitrator (Obergruppenführer Goodell) unless one of four conditions are met.
And those are tightly defined.
So when the OP quotes the article "where there was evident partiality or corruption in the arbitrators" and asks "Could that have been any more clear?" s/he has totally missed the legal point.
It's "evident partiality" if an arbitrator is adjudicating between two parties and is (say) the brother-in-law of one of them. "Corruption", likewise, is the receipt of inducements from one side or the other. The fact that the arbitrator is prejudiced and out to get Brady (as we would all agree is the case) doesn't cut the mustard legally.
So the conclusion of the article is that Brady may be screwed legally.
What's the good news to set against that?
Well, first of all, if that's the legal position as the judge understands it, why is he going into all this stuff about the NFL's evidence? Kurlantzick's explanation (the judge knows that all of this stuff doesn't matter but he's asking the questions anyway because he feels bad at having to rule in a way that upholds an obvious injustice) is bizarre.
Of course, it may be true -- bizarre things happen in courts all the time -- but it's wildly implausible.
At this point, I should say that I personally would MUCH rather have an outcome in which the judge says: "Mr Brady, it breaks my heart, you've obviously been railroaded but there's nothing I can do for you" than one in which (for example) Brady accepts a fine but leaves the question of guilt or innocence moot. Brady's reputation means more to me (and, in the end, I think, to him) than even a four-game suspension.
Still, I think there's another interpretation, the one we get from another sports law professor, Michael McCann. On that interpretation, the judge is asking about the evidence because he's thinking that, even if it's a Section 46 case and Goodell is a legitimate arbitrator, the law won't let him do whatever he likes.
Note that the cases about arbitration Kurlantzick and the NFL are drawing on are all about arbitrators who adjudicate between two parties who are in conflict about the division of costs and benefits (usually money). But in this case Goodell is acting in a quasi-judicial capacity: he's judging wrongdoing on Brady's part. And that's a completely different ball-game.
If McCann is right, Berman asking about the evidence shows that he's concerned whether Jolly Roger has acted reasonably. When he tweets back to RLCarr/Quantum Mechanic "The professor offers sensible reading of situation, but may be overlooking possibility judge views the evidence as part of process." I take the first part of the sentence to be saying "He's another sports law professor and I'm not going to make an enemy I don't need" but the second part contradicts everything Kurlantzick is pushing. It's saying, first, that the judge will look at the fairness of the process (not just whether the adjudicator is "evidently partial") and, second, that building a case on totally inadequate evidence may itself be enough to show that the process is unfair.
In which case, quite simply ... Hallelujah!