I usually rinse and pat dry, especially after brining. As for a mess, just opening the bag that they come in can at times be pretty messy. As for splatter, I don't take it to a car wash. Having both the Serve Safe and HACCP certificates, I do keep an eye on things and the bleach spray bottle and bleach bucket is always near as cross contamination is always a concern.
There are times that common sense just needs to be used. When moving one type of food from one station to another, that's what they make bowls and containers for. It's not like you pick a dripping wet chicken up by the feet and waltz on to the next station leaving a trail of water behind.