This is for a dog who is how old? If I'm not mistaken, your pup is still young enough to be teething...
Personally, I don't think it's all about "I win. No, you win". I really don't think dogs lay awake nights trying to conjure up ways to beat us and be "alpha". I don't think everything is a contest.
I *do* believe in teaching a drop-it command and a leave-it command. Joey does these extremely well. But, he's never been punished for non-compliance (other than not getting a treat). It's been taught strictly based on rewards for obeying.
There are those who think that the order you go down the stairs or out the door determines who is the "winner". I don't. There are those who think that a dog jumping up and trying to lick your face is showing dominance. I don't. Like many others, I think it's an appeasement behavior. There are those who think that when a dog stops struggling, he is showing submission. I don't. I think he's given up.
I must say that this is the first time I've heard of someone thinking that a puppy chewing on you is showing dominance. I don't. I don't think that any more of a puppy than I do of a human baby. I think they are teething, their gums hurt, and chewing makes it feel better.
I do think there are a lot of conspiracies in the world. I don't think that dogs are part of them.
But, that's just me...