Well, on a bike I spend a lot of time paying attention to my surroundings to avoid being in an accident (or on purpose). Riding sick would reduce my awareness thereby leaving me a lot more open to being injured or killed. Part of it is that riding a bike is a bit more involved with clutch and shifting, brake and throttle, rear brake. Plus gear like the helmet will be distracting, especially if you have a headache or sinus infection. Heck, a sneeze will fill the shield with phlegm leaving you in even more danger as you try to clear it (or just deal with flipping up the shield before sneezing).
With a car, or truck, I am a bit more comfortable. Less riding related stuff to distract me. I'm larger so folks are more likely to see me so I'm less worried about someone coming into my lane by surprise and me having to react. I can add heat, wear a scarf, and even sneeze and blow my nose without a problem. I can drink tea when driving to help relieve any discomfort and I think, be a safer driver.
Which is not to say I would do that anyway but it depends on just how sick or tired I am.
Carl