Not that I disagree with you, mammamia, but for me it's in large part about the comfort and care of the child, also. I know when I am sick, I just want to be in my jammies in my own bed. I don't see why a little person would be any different. And if I am devoting all of my attention to one child, because they are ill and deserve that extra attention, I don't want to feel like I am taking away from the other kids to do so.
I am sure that your parents all love that you have that policy, though. I hate having to call and say "come get your kiddo", because it's not usually taken well!!