Add me to the camp of not understanding the issue. I do get that spending a significant time online while home sick can be misconstrued as faking the illness, but not all illnesses are created equal. If, for example, I have a severe cold, I may not be up to going to work and spending time at meetings, walking around, dealing with customers, etc. But can be perfectly fine laying in bed or on the couch and can check email, post on facebook, watch tv, etc.
I rarely call in sick and when I do, it's because I'm really sick. Even in those cases, I'm usually willing to answer email and/or take a phone call (if I'm awake), so I don't see anything wrong with posting on FB either. I just don't think there's a set rule of what activities can and cannot be done while home sick...at least not when talking about etiquette. And where some things are obvious (like riding roller coasters, going skiing, etc), others (pretty much anything done at home) are not.