Jewish custom is to have two separate preparation areas in the kitchen - one for meat and another for everything else. Not a bad idea if you can afford to do so.
Hand to mouth is certainly one way to transfer the organisms to your body, but so too is underdone chicken. Plenty of people have suffered from salmonella poisoning after eating chicken they didn't prepare themselves.
The unwanted bacteria can easily transfer from the surface to the inside of the meat through the removed hair follicles or simply via a knife that has cut the meat.
