Just because they don't go to the doctor doesn't mean the have to come into the office, unless you have a terrible employer...
I hate policies that require a doctors note. Yeah, I have the flu, going to the doctor is just going to spread it, unless I have some sort of complication.
True, but I think they are both symptoms of skimping on medical care, which I don't think people should have to do in general. (I would be happy to pay more taxes to make that happen.) I especially think people shouldn't ration medical care where I work; I suspect the median annual income here is closer to $200k than to $100k.
When you are sick, don't go to work. If there is any question of if the doctor can help, talk to the doctor. (Via phone or video chat, if necessary)