That is why most states are "at-will", meaning that they don't need to list any reason. I am not saying that they could not fire me; they certainly could have. They simply cannot list the reason officially as "because you told people about this event that happened and gave your opinion on it".
If they said "we believe the employee is violent and threatening" that would be a valid reason. I am not. I may get upset and stressed but I have never laid a hand on anyone in my life. There is no evidence to support the claim that I am violent, because it isn't true.
There are also more complex things going on here than just whether or not I can be fired and they can "get away with it". The real issue is that they don't want anyone to know what happened because it makes them look bad.
For that, it actually doesn't matter if I am a raving lunatic or not. The simple fact is they want to cover up the whole situation and make it go away. That is the worst part of all of it.
I'm generally on your side here, but that statement is absolute bullshit. Your employer also has the right of free association, and can choose to no longer associate with someone who states they wish they could commit violent acts against their coworkers, regardless of how serious those statements are.