Mike, I want to congratulate you for capitulating on four-kneed elephants. It's not always easy to admit when you're wrong, but I'm glad you're getting the practice.
Just to throw you a bone, as I understand it, "dominance" scientifically means "better access to resources". What you described actually does sound like dominance: Eddie wants toys, and Eddie gets toys.
For me, I bristle a bit whenever I hear "dominance" or "alpha" because it's used in many different situations and never seems to mean exactly the same thing. A lot of times, it seems like any unwanted behavior is described as dominance. I remember when I got Thor, I thought he was asserting dominance, but I realize now that he's softer than a hot marshmellow. I'm really glad I read up on dog body language because it helped me realize that Thor is constantly giving appeasement signals. I also tried the alpha roll on Thor a few times, and I feel bad about it now. All it did was scare him.
However, for all his softness, Thor does guard me, and that's been getting worse. He used to just guard me from other dogs, and he's started guarding me from people, even people he knows well. Which is off the point, but I guess I mean that dogs can be passive in some situations and aggressive in others.