RE: How could you
Unless you get feces into the body cavity, the odds of any dangerous bacteria infiltrating the meat is slim to none. The only bacteria that will get onto the meat are bacteria that live in the air which you breathe in with every breath. If it doesn't make you sick breathing it, odds are eating it won't either.
Also, nearly all meat is frozen at some point. This effectively kills the majority of all bacteria and viruses.
The only time I ever ice pack my deer is if it's going to be a long period of time >3 days until I am going to get it to processing or if the temp is >40 degrees like it was in Iowa this year. I've never had any problems with anyone getting sick from eating professionally processed deer meat.
Long story short, be ticked all you want about the out-of-towners hunting by you, but them driving off with their deer open to the air has as much chance of making them sick as you farting in their general direction.