I’ve long believed that they do. If you can smell your poo then it’s airborne and if your toothbrush is exposed to that air then there’s a minute amount of poo on there and it will end up in your mouth. This is why I keep my toothbrush in the kitchen where it doesn’t smell like arse.
Call me old fashioned but I don’t want anyone’s poo in my mouth including my own. Kinda makes it funnier when it reeks knowing that your poo is ultimately going to end up in somebody’s mouth though.