I don't think you're right. They might run off to find food, but having found it, they'd be back. My two dogs are less important to me than my own kids, but they definitely beat everyone else. Every day they make me laugh, they give me hugs (doggy hugs are nearly as good as man hugs---depending on the man, often better), they cheer me up when I need it, they sneer at the same TV shows I hate, they warn me of approaching annoyances (like my neighbor, an amiable drunk who invents reasons to drop over at 2 a.m.), and my beagle used to bring me dead possums that she killed especially for me! Not that I encouraged that or anything.
My friend Elaine has a parrot, and whenever I go to her place she lets it out of the cage and for the rest of the day it stays perched on my shoulder, with its little claws digging in for dear life. I feel like a pirate.