Any business you run, there are rules to firing someone. If you dont follow those rules then you can be sued. The NFL is no different, thats why they have to have rules and contracts that both sides agree too. If Goodell doesnt not follow the contract that he sign with the players then he is at fault. Goodell fined them for reasons which he could not because of the contract he agreed too. When parties sign contracts, it goes for both sides. I cant make up stuff along the way. Goodell did not suspend Vilma or any Saints players for hurting anyone (he really does not have any proof). He suspended Vilma and others for paying for play, meaning that the players can not pay each other nothing for any performance good or bad. This reasoning for suspension was not legal for Goodell to rule on.
How would you feel if the company you worked for suspended you with no pay because a co worker told upper management you peed in the bathroom sink. Which what almost happened at my job, but because there was no proof that someone pissed in the sink and who did it other than hersay, they can not be fired eve if they believed it. Or what if you and a co worker made a bet on who can make the most sales, the loser has to buy the winner lunch.
What most companies would do is, find something else to fire you for like attendence or raising goals and expectations that you can not meet.