In any other real life situation, I would totally agree with you, but this is the FA and the have a ridiculously successful record in turning accusations into convictions, he's getting banned for sure.
What is the burden of proof in sporting courts of arbitration? It's not beyond reasonable doubt as would be in criminal court, I think it's slightly higher than just balance of probabilities iirc but there doesn't have to be cast iron proof for them to convict
It's ‘comfortable satisfaction’, which is defined as lying in between the criminal ‘beyond reasonable doubt’ and the civil ‘balance of probabilities’. Interestingly they aren't bound by rules of evidence.