some insurance companies, ie in the 3rd parties case, would most likely want to not have to involve eds insurance company or anyone else for that matter as it will be more costly for them that way.
Because it is clear cut that its not eds fault, they will want to fix the car, and give him a courtesy car in the mean time and hope that will keep ed happy.
If eds insurance company or a accident managemt firm get involved, they will start claiming for inconvience expenses etc, something which ed migth not do on his own accord.