Another reason to wash them out is to get rid of the blood around the area where the bullet hit. I cut out all the blood shot area and wash to get the blood out of there. It also helps getting the meat started cooling quicker. Drip for half an hour or so and into the cooler for a few days. When I was young and the butcher came around he always washed the carcass down with water if it was available.
Having clean water under pressure available when butchering is a luxury indeed.