You're not wrong, but it's more complicated than that. Some Japanese wear them for fashion reasons, just because everybody else is wearing one. Some (usually women) because wearing a mask means you don't have to wear lipstick in public, which means you can get out the door faster in the morning. And a lot of people (wrongly) believe that a mask helps keep you from getting sick. If only the sick wore them you wouldn't see nearly as many as you do on the streets in Tokyo.