Who does your dog think you are?

I've noticed my chihuahua will show her teeth to other people, but she never does it to me. I've read that dogs will do that to show dominance. Luckily, most people just think it's cute since she's so small, and usually she does it while licking them to death anyway. She's very friendly, even to new people, she doesn't growl at them or anything hostile like that. I like to think that she doesn't do it to me because she thinks of me as her alpha dog. Does anyone know if I'm right about this?