I say do what works for you. My dogs share toys. Ellie is "alpha", but I'm still not going to let her keep a toy when it's Rylee's turn. She is pretty good about sharing toys. I look at it this way. Eddie may be alpha over Jillie, but you are alpha over them all (if we're going with this theory). At any time you can decide it's Jillie's turn to play with a certain thing whether Eddie likes it or not. You decide, not him... I could see how this could start a fight, but in my kingdom here
I require sharing.
If the dog that bit Rylee's ear had been given both chews, there wouldn't have been a problem, so in that way I can see how a possessive dog could give another dog a beating for having something they wanted. But I don't feel that is always fair to "underdog". Canine system or not, IMO that is trying to run things and I don't like it. But if the pups here were to go at it over a chew, they would be picked up. And they are never left alone together.