Actually, the only thing that was "appealed" to the court was whether or not the NFL was "allowed" to take the actions that they took under the terms of the CBA. Therefore, there should be no discussion of burden of proof or evidence as it relates to guilt or innocence. Just a standard interpretation of the terms of the contract and whether or not those terms are valid and were applied in this case in the manner proscribed in the contract.
But hey, what's wrong with a little red herring like "burden of proof" and "evidence".
And when the burden of proof is based on a preponderance of evidence it does not require a lot. There is more than enough to cover the burden in this case.