I'd almost agree with you, but I think the biggest thing is... if someone's sleeping on the street, in their car etc... you can probably assume they don't have much in the way of family or friends that are willing to step up and help out.
Meaning they can only really surrender it to pet shelters... which we all know have a huge influx of dogs, and the older the dog, the lower it's odds of finding a loving home, the higher the odds it's just going to be killed.
So yeah in short, one the dog probably is probably not as shaken by being homeless as it's human companion, and even if it's not, that's still probably the least bad option for it.
If a homeless man has a rich cousin that says "Sorry man nothing I can do for you, but my kids really want your 8 year old german sheppard" and the homeless guy says no I need him with me, I'd respect him less. But I have to say, in most cases keeping the dog and master together is more often than not the best outcome for both of them.
Flying pig was too on the nose?