A few points I'd like to add.
First, many people in this thread have debated the safety of hunting. I'm not really sure that's the relevant issue. The key is whether Cheney's own conduct amounted to negligence when he pulled the trigger. For example, driving is a potentially dangerous activity, but millions of people perform it safely each day. When an accident does occur, you don't say "they were engaging in a dangerous activity by guiding a 2,000 pound steel instrument at 60 m.p.h., so they must be guilty." Rather, you ask "were they driving safely this time, in this situation?" Regardless of the overall risk of hunting, the only thing that really matters is whether Cheney was performing this particular activity competently. If hunting is a more dangerous activity, that simply means that he should have exercised more care when doing it. But his individual actions are still the key. Although he could still be possibly found negligent, everything I've read so far suggests that it was a true, reasonable accident.
Second, various people have mentioned that the press released private information about the victim's health. I'm not sure that's true. I think that the press has actually been fairly reserved in its reporting - no pictures, no torrid descriptions. Just enough of an explanation to get the idea across.
As to whether the event itself is newsworthy, it unquestionably is. If the vice president accidentally struck and seriously injured a pedestrian while driving, no one can doubt that it would be a newsworthy event. This is similar. (If anything, it's worse. After all, driving has some utility because it gets you from place to place; hunting's just for fun. To cut off any objections, I know that some people hunt for food - but I'm pretty sure that Cheney's hunt was just for fun).
Finally, the press isn't so much worried about the fact that the VP shot someone as they are about the way that the White House handled the incident. Apparently, the White House felt that it was acceptable to utilize a private citizen to announce that the VP had just shot someone. Moreover, the citizen made the announcement only to a local newspaper, and only after an entire day had passed.
This really raises two problems. First, taking so long to report the incident simply makes it look like the White House was trying to buy time to see if the story would die quietly without being reported. Regardless of whether that was their intent, their actions created that appearance.
Second, the press is concerned because it feels that this sort of information should be disseminated by a single, reliable point of contact. If the White House starts to use random private individuals as a vehicle to announce official news, how would we ever know whose statements to trust? Could you ever discredit your crazy neighbor's statements about the president's health? After all, she might be the very individual the White House has chosen to officially announce this news! When anyone can speak on behalf of the president, everyone's statement appears equally legitimate and you have no idea who you should ultimately trust.
In dealing with an incident like this, there's real value in transparency, immediacy and a single point of contact. All were lacking here, and *that's* what bothered the press.