Let it Be

I heard screeching from upstairs.  The dude was here cleaning the contents of Miss A's dinner plate off of our new micro-suede kitchen chairs. (Good thing we bought the stain-guard warranty!!!) So I run up the stairs, two-at-a-time and throw open the bedroom door and find Miss A and Little E engaged in sort of a kid/toddler cage match thing over a doll.  They are laying across a pillow - limbs entangled, blood-curdling screams, flopping around like two fish out of water. 
I say, "What's going on in here?"  Miss A says, "Nothing!" and hops up really quick.  Little E not so worried about who is to blame and/or getting in trouble; starts screaming and throws herself dramatically down on top of the doll, shouting "IT'S MINE!"  Know what I did?  I said, "Hmmph.  Okay.  Well, it's almost nap time.  I'll be back."  And then walked back downstairs to address the chair cleaning guy. 
Want to know what I heard next?  Nothing.  Silence.  By not addressing the situation, I seemed to have diffused it.  I brought no energy into it, therefore seemingly, did not fuel it any further.  Now, ordinarily I would have completely intervened.  I would have positioned myself between them physically and then went on and on about the whole, "we need to share, we need to be kind, blah, blah, blah" routine.  But I'm pretty sure they already know that stuff.  In fact, I know they know that stuff, but in the heat of the moment, it flies out the window - just like it does for many adults as well.  We know what we should do in most situations.  We know when we should keep our cool, but sometimes we just don't.  We get caught up in whatever the situation is and we sometimes don't always react appropriately.  Or maybe you do - but I know I don't always. 
So my question is, why is it that I sometimes hold my children to a higher standard?  Especially given the fact that they are CHILDREN.  They are only beginning to learn how the world works - and what is and isn't acceptable.  So while I do believe it is my job to tell them the difference between right and wrong, I think it must also by my job to let them figure it out on their own to some extent.  I won't let it get violent or ugly by any means...but sometimes I think beating that theoretical dead horse is more counterproductive to the situation.  Because given the evidence today - they didn't need me to solve anything.  They didn't need me to tell them anything about the fact that they were acting inappropriately.  They knew.  And instead of getting completely caught up in defending themselves to me and pointing fingers at who was right and wrong, which would have completely escalated the situation - they just let it go.   Very interesting.  What's your take?