As far as DUI's go, that would pretty much be an insta-fire for my company, because many of our guys have to drive company vehicles or travel to job sites that are not transit accessible. If the employee is an otherwise good one, then maybe an exception can be made depending on circumstances, but that's a pretty huge knock against someone.
If I found out one of my guys got arrested and charged for beating the shit out of his wife? Yeah, I'd have a hard time hanging on to him. First because of the personal distaste I would have for it, second because of the potential impact on my company's reputation ("hey, I heard your site supervisor put his wife in the hospital, is that true?"), and third because that obviously means the guy has serious issues and it's only a matter of time until something else comes along.
For professional athletes, they are public figures. Keeping their lives together is part and parcel of being an athlete. If you can't manage that, then yes, don't be surprised when you're out on your ass because your team doesn't want to be associated with your radioactive public persona.