That would be asking for disaster now, even in a wilderness area. It probably was foolish 30 or so years ago. I recall one backpack adventure into the Bob Marshall Wilderness of Montana when my partner got sick. I am going to guess it was a water problem, even though we didn't see another person within miles of where we camped. The Hiker Alert warns that a number of gastrointestinal diseases can be passed from person to person through shared food, shared utensils and personal contact.
Hand washing is important.
So is the washing of soiled articles of clothing. Hikers should take special precautions around their ill peers. Norwalk-like viruses are primarily spread through direct contact with vomit or feces from an infected person. Their route of entry is hands to mouth. An infected person can spread the virus for up to two days after the diarrhea or vomiting stops.