I'm not sure if all director owns the copyright or not. It's probably different for each project.
Directors sell neutered versions of their work all the time under the "director's cut" rubic. But these films tend to be extreme, such as Natural Born Killers, etc.
Figure a borderline movie for a lot of people -- Chicago --in which there is one graphic implied sex scene at the beginning would be the ideal candidate.
Also, the director would have more control over the way in which the "offending" material was cut.
Yeah, but they sell the versions for airing on TV and airlines not for sale. Many directors won't allow their films to be altered for airlines.