I think it has a lot to do with how close the dogs were as to how much 'grief' they will experience. In a household where there are several youngish dogs who all play together with one another, the disappearence of one of their number might no be that keenly felt by the others. Where breeders I know have rehomed dogs, the remaining ones have not appeared undually concerned that someone has gone, and the same appears true when there is a death that the other dogs do not witness. On the other hand, where there are two pet dogs who have lived the majority of their lives together and one suddenly goes, surely it is only natural the other will miss the loss of a companion? Dogs also pick up very quickly on human grief so the combination of the other dog and owner's distress may well cause the remaining dog considerable stress.
One of the reasons I am looking to get a new pup at this point in my boys' lives is that when the dreadful day comes to say goodbye, the remaining dog will hopefully have an established companion so he is not left alone. I don't think I could cope with a grieving dog as well as my own grief. Where I have had rabbits living together and one has died naturally, the other seems to accept it much better than if was PTS at the vets.
It's slightly off topic, but altough it sounds morbid and has been dreadfully had to think about, I have made all the desicions about what is going to happen when the end comes. If I have the option (ie not surgery) I will call the vet to the house rather than taking them to the surgery as I want them to go in familiar surroundings and I have also looked into where to get the cremation done, as some places are better than others. I just don't want to be faced with making difficult desicions and possibly ones I will regret when I am trying to come to terms with losing my boys.
One of the things I envy dogs for is their lack of perception about the future. They just take each day as it comes and don't worry about what might be around the corner

Its a good philosophy to live by

I just wish I could do it!