I think you read more into this than it deserves. Cops don't want to look like they are catering to the wealthy. You put them on the spot and nothing in the way of celebrity will stop them from treating you like a regular citizen.
Lots of videos on youtube showing cops refusing to give special treatment.
This is not a domestic case. The driver is not related to Angie Harmon.
Relations have nothing to do with it. A domestic disturbance is what this is. A disturbance at a domicile. Sometimes it involves neighbors. In this case it involved a delivery guy who is likely fired, possibly going to get sued, and maybe even charged with a crime.
You appear to be stretching. Domestic cases have everything to do with relationships, almost nothing to do with locations. Burglaries, home invasions, arson all can happen at residences, and not be anything domestic. Happening at a domicile is not the definition of a domestic case. This case did not even happen in the domicile, and may not have happened on private property, although such is not immediately clear. The driver might have been on private property when it happened.