As far as I can tell switching between first and third our eyes are in our foreheads in first. There is nothing wrong with the first person camera.
All I know is that this isn't true in my game for my male altmer character (the only one I've created so I don't have any basis for comparison). If I stand face to face with Lydia, for example, my character's eyes are level with the top of her forhead and she cranes her neck a little to look up to me in third person. But in first person she's not looking up at me. In fact, she appears as tall or perhaps a little taller than my character.
If I'm not mistaken, female characters tend to be a little shorter (I don't feel like loading my game just to confirm) than males, maybe the camera for all characters is set at a height appropriate for female characters so only those playing male characters might notice it?