I agree with your assessment, but unfortunately I've seen far too many groups think like this, and most will attempt to justify it as self-defense.
They can 'justify' it all they want. When the consequences of that action kick in, they'll probably get the message. Not that I would let it get that far as a DM, because there would be a very clear warning that comes first, and I would be very clear that this path (once started down) cant be undone.
Players only do stupid childish like this because DMs all too often dont enforce the consequences. After the player murders the bouncer, have a wail come up from the corner of the tavern as the bouncers wife starts uncontrollably sobbing, holding a baby in her arms, and asking
why why why! as tears stream from her eyes. Roleplay it. Have her approach the PC and flail at him screaming
murderer!. Have patrons react accordingly. Reinforce the horror of what the PC has just done. Have everyone react like the monster he is. Have children hiding behind mothers, and several townsfolk race out the door to alert the local Lord that a mercenary band of stateless vagabonds have just killed Bob the Bouncer.
This kind of behaviour from players is always down to the DM.
Actions should have consequences.
The fact is, it would appear that the DM did not introduce any immediate consequences to the act. The player appears to not feel that there is any real problem with the act in the first place, and seems to feel that his action was justified as well.
And I would stamp down on that behaviour as a DM it wouldnt be funny. As a sidenote, I would as a
player as well. If another player at the table was about to do something like this, I would advise him (player to player) that this means the end of his character and my character travelling together, and in light of that ask him to rethink his actions and the character he is portraying.
I highly doubt (unless I was playing an Evil PC, and even then its dubious) that I would want to travel with such a villian. He's a sociopathic monster prepared to murder a man (and in full view of others). There is no way I could trust him from that point onwards at a bare minimum.