How GAs are handling the non-security players is fine. Though GAs shouldn't jump on the ban wagon until information is fully gathered. If it was self defense, it should be looked away the first time but warn that they shouldn't our right kill or arrest the said antag. Should be treated like the blueshield does with command, stun the threat and get away. If you want to kill or hunt antags, join as an officer.
Officers should know SoP, this isn't a get-away-free ticket to kill antags, follow the proper procedures before you go killing someone.
I feel some information is left out and are quick to judge on what is going on. I honestly don't think punishment shouldn't change, but getting a fully story before committing.
EDIT: For antags, if someone is straight up after them, same applies. Just stun them and retreat if it isn't part of your objectives. As long as they don't commit to killing. If they do kill that greytide or whomever is chasing them, should hear out why they did it and judge if the action was appropriate, which GAs already do. Honestly think, they should not hide the bodies though. Make it so they can be revive easily. If they get attacked by same person, it should be reported for valid-hunting