You're saying that the league never said anything about Brady being uncooperative or less than forthright when they originally suspended him? That's not what I recall.
"With respect to your particular involvement, the report established that there is substantial and credible evidence to conclude you were at least generally aware of the actions of the Patriots' employees involved in the deflation of the footballs and that it was unlikely that their actions were done without your knowledge. Moreover,
the report documents your failure to cooperate fully and candidly with the investigation, including by refusing to produce any relevant electronic evidence (emails, texts, etc.), despite being offered extraordinary safeguards by the investigators to protect unrelated personal information, and by providing testimony that the report concludes was not plausible and contradicted by other evidence."
The NFL release cites as their authority for the punishment the "Integrity of the Game Policy" which is applied to teams, not to players, and is not a part of the CBA that governs the relationship between the league and the players.
There is no punishment under the CBA for "failure to cooperate fully and candidly." Further, there's no precedent at all for punishing lack of cooperation with a suspension. Favre got a fine.
Anyway, based on everything that has been released, it sounds like the alleged "failure to cooperate" is a fabrication, since Tom Brady actually did produce vast amounts of relevant electronic evidence. He just didn't produce the evidence they were hoping to find that would clearly incriminate Brady and also implicate higher up members of the organization.
It really sounds like the NFL was operating from the assumption that the Patriots, and Brady specifically, were guilty, which means that "You didn't produce evidence that would clearly show your guilt or admit you cheated" becomes "You didn't cooperate with our investigation and your statements were not credible."