Okay - So I have the same issue on my E92 Coupe. It's a "cornering at low speed" situation and I get a rubbing groan sound - sort of a humming. I hear it daily when I turn into a parking place.
I knew it was the diff when I first heard it, but for a few minutes I thought it might be a wheel rubbing in its wheel well. I also wondered if some lug nuts were loose causing a rear wheel to rock up against the interior well wall.
As a group, what have we decided? Let it be or get more diff fluid in the unit?
I have 2700 miles, but it doesn't sound like something that will go away, more likely something that will increase over time. Friction increases, it doesn't go away over time.