Untrue. When I used to moderate the Pokémon Animé forum, I always based my decisions on how I was feeling at the moment which is why sometimes I would let people fight and other times I would not. I found that they react well to that and stop causing problems quickly. That's why members like Jolene, Advancedk47, and weedle_mchairybug stopped trolling that forum since I would call them out in public and in private. Plus, it's fun to do that especially when they try to argue with you about it. It actually let's you do something in there.
Maybe untrue for you since that is how you go about your business. Different mods have different modding styles on almost every site I have been on. I don't tend too base my decisions on my mood but the rules in place for either the entire site itself of the current sub forum I would be dealing with at the time. On the subject of allowing them to fight some times and dealing with them others was it actual fighting or was it a heated debate? If they were getting personal with each other then I would step in. If it is fighting were they take it personally then I tell them too take it too the pms or cut it out altogether. I am all for calling people out, not too the point of making them look like complete and utter dumbasses, but to get the point across that they actions don't need to be repeated, and if the user does then repercussions in the future will follow.