Obviously I have read the same things as many on this board. I often have discussions with my "old school" dog training friend on the merits or demerits of the "dominance" issue.
I don't think most people who say they have "aggressive" dogs have truly dominant-aggressive dogs. They are fearful dogs.
I think dog/human interaction is much more, as has been described, of a parent-child relation. A parent does not have to resort to yelling and corporal punishment to establish their authority.
In dog/dog relationships there does seem to be a hierarchy. But it changes on what other dogs are around, where they are and how tired/excited everyone is at the time.
Example. My friend has an older dog and a year old puppy. When they come over, my dogs will growl and show teeth at the overly exuberant puppy who wants to get in their faces, but never do that to the older dog. When the puppy is calm he is allowed to get close. But he doesnt' seem to catch on very readily to dog language. I don't think my dogs are aggressive or dominant, even the oldest bitch who is even LESS tolerant than the others. They do not like the puppy in their face. I can understand that.