Hey! I think that it varies depending on the dog. I don't believe dogs see us the same way they would see their siblings in a litter or in a "pack". this is just a matter of (like you said) normal puppy behavior that happens to be inappropriate and all you need to do is teach the pup that the chew, toy etc. is appropriate.
Ways that I would combat this is to have treats handy when the puppy is playing. once she starts biting or mouthing, I would pull away, wait until she doesn't offer the bite, then mark with a big "yes" and reward with treats and praise. then I would substitute the toy. the treat=positive reward, and this creates a positive association and increased desire for the toy. It's just a matter of teaching! I know this isn't going to be popular opinion, and there will likely be several that argue the "alpha/dominant/pack-leader" theories, but like I said I don't believe dogs view us in that way. Hope this helps!