It turns out astronauts pass colds and other diseases around the capsule with great abandon. Read all about it in this Time article.
I've always wondered what happened if an astronaut got appendicitis or has a gall bladder attack - things that happen to otherwise healthy people. I expect there is no way to do open-gut surgery in a spacecraft. Perhaps they take out appendices and check for gall and kidney stones before sending astronauts aloft?