Clinton has a lobar pneumonia. The most common bacteria that cause that type of pneumonia are all part of the normal human bacterial flora that lives in the airway. None of them are contagious in the sense that if she were to cough on someone, they would get pneumonia. People seem to think the contagiousness of tuberculosis is applicable to other causes of pneumonia. It is not (and for the nutters, she does not have TB since she is not receiving the four drug regimen for it). If she had a preceding viral infection that predisposed her to getting pneumonia (this time of year it is typically rhinovirus/enterovirus, ie the common cold), the virus could be contagious but that would be before the onset of the pneumonia.
As part of the CDC recommendations, any patient admitted to the hospital with
bacterial pneumonia (even if the pathogen is unknown) or viral pneumonia are placed on standard precautions, meaning nobody has to wear a mask, gown or gloves to see the patient. Even in viral pneumonia, adults shed much lower quantities of virus that children. Kids really are the transmission vector of so many illnesses.
http://www.cdc.gov/hicpac/2007ip/2007ip_appenda.html