How did you react to your reportees verbal duel?

How did you react last time when two of your reportees got into a verbal duel in your presence, where the volume was high and the tone bordered around distrust?

When it happened to me I felt glad. No, my sadism hasn't got the better of me yet :) my reasoning is that 

1. If they could argue in my presence means there is a comfort to voice out differences when I am around. We can call it their guts or culture of the organization.

2. I got the opportunity to listen to both sides in person and sort it out right there. There wasn't an opportunity for the whole organization to know before the boss got to know

3. I did not have to hear it from a third person which would have come in the form of their interpretation than what was said and why. 

But, most of our reportee fights (#email, calls, during meetings) are in our absence. The people who report them first to you sometimes get the advantage of your bias towards them. So, how do you feel when these verbal fights happen in your presence? I found myself blushing, embarrassed, helpless to state a few.  I wished I wasn't there.

I also felt we should have a culture where we shouldn't even get there. But, it isn't a workplace if people can't express themselves. The problem is the how!