This belongs completely in the realm of speculation, but it is speculation based on my own experiences as a criminal lawyer. Why would a media-savvy and clever man like Dick Cheney delay notifying the press and the police about an accident when a) he knew it would eventually be covered by the press and b) he knew he would be criticized for delaying release of the story? A simple cost/benefit analysis suggests that he (or those advising him) must have believed that there was more to be gained than lost by a 14 hour delay that would eventually be made public. It is likely, therefore, that something happened during that 14 hour period which was worth the negative costs of the delay.
What is the most likely thing to happen during a 14 hour delay that is worth the negative publicity? One possibility is that it takes approximately that period of time for alcohol to dissipate in the body and no longer be subject to accurate testing. It is fairly common for people involved in alcohol-related accidents to delay reporting them until the alcohol has left the body. There is no hard evidence that this is what happened here, but we are entitled to a better explanation. We should be told whether Vice President Cheney's victim had alcohol in his system when he was taken to the hospital. Was there any alcohol at or near the hunting area? Were any in the hunting party carrying flasks (which is apparently common among hunters)? What was Cheney doing just before he went hunting? Did anyone in the hunting party have a drink? We do know that Cheney had two drunk driving convictions when he was in his early 20s, but he has apparently been clean since then.
There are certainly other explanations for the 14 hour delay, but simply postponing the inevitable publication of a damaging story is not one of them. Nor is the fact that Cheney is, by nature, a secretive man. The burden of proof has now shifted to the Vice President to explain why he made this stupid, or very clever, decision. We're waiting for his explanation.