I think there's a good chance someone or several someones from the Patriots, possibly including Tom Brady, knew and/or had something to do with the low pressure in some of the footballs used by the Patriots during the 2014-15 NFL season and playoffs.
But a good chance is not a very high standard.
Further, I'm not sure that the standard of proof for civil litigation (preponderance of the evidence? balancing of the probabilities? it depends on who you talk to) would find against the Patriots. It might, though.
That doesn't mean that by some standard, such as "more likely than not" the NFL erred in their finding. It's just a question of what standard should be used.
As I wrote over a decade ago, the appropriate standard of proof for different institutions and different legal environments requires an understanding of confidence intervals, Type I errors, and Type II errors.
With the weakest standard of proof, call it the "more likely than not" standard, we are willing to tolerate a higher probability of "convictions" (that's not really what they always are) of innocent people in order to make sure that there is a higher probability of punishing those who actually do commit an offense. We don't tolerate such a low standard of proof in criminal cases, not wanting to punish someone who is probably innocent. (see my piece on cruel and unusual punishment)
But in internal disputes (like the NFL and the Patriots) presumably the standard of proof for offenses and punishments is set out in franchise agreements and player contracts. Given the Patriots' response, and given the analysis by Russ Roberts, I really doubt if anyone involved with the Patriots is guilty beyond a reasonable doubt. At the same time, I think there's a chance someone involved with the Patriots did something.
And if all it takes for the NFL to levy fines and punishments is a low standard of proof to the tune of "Palmer thinks there's a good chance someone did something wrong," then while the fines and punishments may be reduced, they will not necessarily be rescinded completely.
Note: I have only a two-week law degree and so I'm quite open to refinements to the above from my lawyer friends.