When camping near our transportation, if someone has a problem where they would be better off at home, we would probably leave. That being said, with a lot of problems such as a cold, you will be miserable either place, so unless our circumstances contributed to the problem, (snow, ice, rain, etc.) we would probably stay. I know I can shake a cold faster out in that nice fresh air than sitting at home wussing in front of a TV.
When backpacking, you have more chance of getting home later than leaving early. Depending on group size, we may divy up some weight for the sick person, and slow the pace a little, but unless it's a real emergency, they still have to get out on their own. Emergency evac can run from $7000-20,000 although most search and rescue groups do not charge. Those guys are heros in my book, and I don't want to waste their time and energy if I have the sniffles.