Doctors have reported the virus can be found in multiple places in the body but not always, some people just get the respiratory illness and others get a digestive illness but nothing in the lungs/etc.
So given the transmission is largely from droplets suspended within bodily fluids, it probably made more sense from a public health standpoint to try identify people with the virus in their nose/throat as they'll be coughing/breathing out those particles whereas most of us don't go around ****ing on people in public so there's probably less risk there.