I think the consensus (that I have read) is that eggs, cooked or raw, are very healthy for dogs. However, salmonella
can be present in raw eggs, and I think that is what causes dogs to get sick. Similar to us when we bake, we shouldn't eat the dough or cake mix if there are eggs since they are not cooked yet and may contain salmonella. Cooked eggs should be totally fine and very nutritious.