@Sarah977
Yes, I know. It seems that some people take it as an affront, almost an insult to their child, that you won't accept them. It's such a strange thing to take personally when it's already listed as a policy and therefore clearly applies to everyone!
I've very rarely received requests from pet owners though. I do remember a girl who wanted to bring her elderly cat who sounded adorable and a guy with a dog who he said was cat friendly, but I had to say no because my cats would freak out if either a dog or another cat was suddenly introduced to the household. These people understood as soon as I explained it to them. I don't ever remember anyone getting irate with me because I said I couldn't accommodate their pet.
Requests from people with kids have been quite different (and far more frequent). I would say that the vast majority of them were not prepared to accept no for an answer, which I find odd. Why would you want your child to stay somewhere that is potentially not safe for them?
When my niece was little, I would watch her like a hawk but you are right, we can't assume that total strangers would do the same. Only recently, I was in a major underground station (London Bridge) and saw a tiny child (don't think she was even three years old) trying to navigate her way down a large flight of stairs amidst rushing commuters. It wasn't clear immediately who she was with.
Okay, her mother was carrying a baby so perhaps it was impossible for her to hold the little girl's hand at the same time, but she was several paces ahead so couldn't even keep an eye on her. Of course I, and several other people stopped, because we we worried for the child. People actually always stop and help a parent when they have buggies etc. to get down the stairs. There are also lifts at that station, so I don't know what the mother was thinking.