It's not about balls.
Correct. Because "having balls" is really about being brave. Facing up to a real world bully is being brave, because that bully might punch you. But, in a mostly-anonymous internet discussion, there's nothing to be brave about, as nobody has any ability to harm anyone else, except by throwing mean words (ooh, scary!). Without consequences, no bravery is required.
Here's an interesting point about the internet. In the physical world, humans have a whole bunch of non-verbal cues and responses to manage and prevent personal clashes. In the virtual world, the majority of those cues aren't present. Egos clash, but the common mechanisms to resolve one way or another aren't there. So, with neither party having any real power in the situation, the clash just continues, often perpetually, often carrying over as a personal grudge from thread to thread.
We've found that our method usually breaks that pattern, by bumping the issue to someone who does have some ability to end the clash, one way or another.
Or, if you need to, you can think about moderator action as being the consequence that drives resolution of conflicts.