I first read this thread the day it was started as I was sitting at home debating whether or not to ride that day. I'd had a bad cold the week before and so worked from home the whole week and stayed off the bike over the weekend. Trying to ease back into things and still fighting a lingering cough I had only biked in one day that week but by that Friday I was starting to really miss riding. I ended up deciding to ride and felt OK. The next morning my cough was worse. I went out for a leisurely ride yesterday, but drove to work today. I'm starting to feel like the cough is never going to go away.
So what does that mean as an answer to the original question? If I feel like riding, I ride. If I don't feel like it, I don't. I'm in a position to have that option. Not everyone is.
I have a theory that fresh air and moderate exercise are good for you, even when you're sick, but I try not to push myself when I've been ill.