...and not exactly like you might think. I have been formulating a theory which helps explain a lot of dog (mostly puppy) behavior. I will present the reasons why puppies would believe it, and what evidence there is to show they do.
Basically, puppies see our hands as mouths. Mouths in the dog sense. Not for eating, but for playing, and touching and picking up and rubbing and generally expressing themselves. Dogs use their mouths for everything, and we use our hands for everything.
The way we have an opposable thumb, they don't get it, it just lets our hand open and close like a mouth. From the very beginning, we're using our hands to rub on them, just as their mom uses her mouth on them. When they bring the ball to us, we grab it with our hand/mouth, as another dog would. This is especially evident when we play tug-of-war. Fingernails could be seen as a hard/sharp spot equivalent to teeth.
This is why I think puppies bite hands. When they play with other puppies and dogs, a big part is biting at each others face/mouth. This is why they might not want their ears handled. In play fighting, a big thing is to keep the other dog from getting your ears, and vice versa, trying to bite the other dog's ears. Dogs also try to grab at each others collars? I've read some pups show aggression at this.
Also, pups are very focused on our hands/mouths and that's why they tend to understand hand signals best when learning tricks. Mouths are a big part of dog body language.
My pup loves to lick at my cats face and nip at her face/ears (especially when she hasn't seen the cat for a while), and the cat hates it, but just bears down and takes it until he can make a break for it, or I come save him. If I tell Pooka NO, she will back off a bit, but if I start petting the cat (usually on his head and ears) showing Pooka to be nice, she gets even more excited and starts doing it again. I figured out that I think she believes I am putting my mouth on the cat and that this is what she needs to do.
(I don't know what pups think of our REAL mouth... They don't think "smiling" is like aggressive "teeth baring", so it kind've shows they don't think of it in the same way as a dog mouth. They also tend to learn its the "OFF LIMITS" mouth. No biting! but great for licking yummy tastes off of!)
That's all I'll say, I'll leave it up to you to provide more evidence for or against my theory. If you think its right, I think it can be helpful to puppy owners trying to figure out how to handle their pup, especially when its in its biting stage.