IIRC there was a study done showing symptomatic and asymptomatic carriers had the same virus load. So while you simple reason is correct, there's not much else if I understand things correctly (please correct if wrong.)
I would be interested to see that study. My understanding is that the WHO, CDC, & EU all say that asymptomatic shedding theoretically possible but highly unlikely?
True! But one of the major means of transportation for that virus is by coughing, which people do rarely if they are asymptomatic. Sharing drinks or other means of liquid transmission still occur, but coughing is the big one as it takes infected throat and lung fluids, and flings them all over everything. Same reason doctors really push using tissues for sneazing if you have a cold.