Interesting that you'd say this -- I think there's always exceptions to these rules, and here's mine:
I had a half-laborador, half-pitbull. Like a lab, she was very aware of people's emotions, and like a pit, she was strong, aggressive, and had a very high pain threshold. (She barely reacted when we pulled porcupine spines out of her nose with pliers.) Unfortunately, this was a problematic mix. If I was the least bit uncomfortable with somebody, even if it was just social anxiety and I wasn't in any danger, she would start growling and try to make them go away. And she viewed every other dog as a mortal threat, to which she would react with murderous fury. I have no doubt that if I had felt physically threatened, she would have done serious and possibly disproportionate damage.
I wasn't able to take her out much.