Grasping at straws. When the initial appeal started, a big deal was made out of how it could go two ways:
1) The entire case is reconsidered. This is essentially retrying the case, there's no deference to the original ruling.
2) Determining if Goodell's ruling was defensible. In this case the conclusion itself is not retried, and therefore no new information is introduced.
The only way a suspension could be supported is by mixing and matching the two: introducing new facts and a new standard of awareness that wasn't present anywhere in the Wells Report, and then simultaneously assigning a ton of deference to Goodell's original decision.
But assuming Berman rules in Brady's favor, the second appeal would presumably follow the same rules. In case 1, there's no deference to Goodell's original decision required. In case 2, the arbitrator would have to rule whether Goodell was correct to suspend Brady for four games based on the contents of the Wells Report.
And since Berman's ruling in Brady's favor would hopefully eviscerate the "general awareness" standard, as well as the lack of notice that Brady could be punished for either "general awareness" or "lack of cooperation, a neutral arbitrator would pretty much have to overturn Goodell's initial decision.
In short: assuming we get the ruling we want from Berman, this won't be as simple as rubber-stamping the same punishment all over again for the NFL. There will be hurdles in getting from the Wells Report to a four game suspension that no truly neutral arbitrator can overcome.