There is nothing wrong with the way the story was handled.
Sure, the MSM is all out of shape, but did you ever stop to consider two things: 1. VP Cheney did not have a public relations person with him to handle a press release; and, 2. He was probably in shock himself. Can you even grasp the enormity of shooting someone - especially a friend.
Just because it was only bird shot, doesn't mean that Mr. Whittington couldn't have been severely injured. Everyone needed time to sort it all out before the exalted press was notified.
After seeing him today, that is my take on it, too.
It is one thing to run the White House Situation Room on 9-11, quite another to shoot your friend.
He seemed devastated to me and either didn't give a damn about contacting the press, regardless of the mess he knew it was going to make, or he decided to take the heat and let his friends have a few hours of peace before the onslaught from the White House Press Clerks.