Did the OP say if the dog was on a public road or on private property?? In my area, on a road is always unavoidable (don't veer for deer) and on private property, it is always avoidable.
If it was on a road, I would grieve it. When it comes to panel say, "If you are going to start making on road dog strikes avoidable crashes, someday, we are going to find a dead UPSer in a ditch somewhere. We aren't going to know why he or she died because the stupid dog he swerved to avoid does not talk."
Putting a truck into a ditch to avoid an animal is stupid, plain and simple. If a boss supports that kind of action, they should get a backhand to the face.