In reality, I would expect the sheriff to arrest both parties caught fighting, and sort out “who started it” later. I mean, both guys are going to say the other one started it, aren’t they?
There are two people watching this fight. So they know who started it. One could argue that they are unreliable as witnesses because they are intoxicated from drinking beer. However, they sound lucid. Also, the Sheriff is not there. Whoever started it will not be caught in the act.
That’s what I mean; he didn’t see who started it, and if he breaks it up and questions the witnesses without securing the fighters, the one who they finger for starting it might react poorly. He’s unlikely to get violent again with the sheriff right there, but it would seem to be an unnecessary risk.