Genes for this or genes for that is just sociobiological claptrap, in my book, a poor excuse for failing to investigate the real causes of things. No, there are no "genes" for dogs saving humans, but dogs are poor distinguishers between "dog" and "not dog" when it comes to pack behaviour. Although I can't lay my hands on the research any more, there was a beautifully done article on domestic dog behaviour in one of the psych journals I read at college. Dogs, apparently, accept that all "creatures" within their "pack" milieu are members of the pack and will very quickly work out their position in the pecking order and then more or less stick to it. Intelligent dogs (such as border collies) appear to be able to make "decisions" about their "instinctive" behaviours dependent on circumstances. They are also very good at working out what is acceptable (and unacceptable) behaviour in the pack environment. Dogs hate uncertainty in social situations and there is a theory that family dogs which bite family members are just uncertain about their position (or "worth") within the pack. Dunno about that, though.

Cats, however, walk alone.

I don't think that any of this is "devious" explanation. You will surely have observed a lot of the behaviour in your own dogs.