A Washington Post researcher dug up this notice that ran on page 3 of the July 18, 1804 edition of the Gettysburg Centinel: "By a gentleman from Philadelphia we learn, that last week a duel took place at New York, between Colonel Aaron Burr, Vice President of the U. States, and General Alexander Hamilton, in which the latter was mortally wounded, and expired in a short time after he was taken from the field. The cause of the duel, or who was the challenger, we did not learn."

So you see there's a long and noble tradition of delaying disclosure when the Vice President shoots someone. Then, as now, the White House understood that the proper way for the public to learn about a shooting involving the Vice President is through rumor and gossip.
[By the way, forget the wild notions you've heard bandied about the Internet that Cheney might have been drinking heavily when he blasted his buddy. He talked to the Sheriff's Office just 18 hours after the shooting incident, and he would still have been measurably intoxicated at that point if he'd had, for example, 24 beers.]
Back to Burr and Hamilton: And as in the Deadeye Dick case, there was much confusion about what exactly transpired shortly after dawn on July 11, 1804 on the bank of the Hudson River. Burr had challenged Hamilton to the duel after taking extreme umbrage over reports that Hamilton had disparaged his character and had referred to certain "despicable" conduct by Burr. Gore Vidal, in "Burr," speculated that Hamilton had alleged that Burr had an incestuous relationship with his daughter. Ron Chernow, in his recent biography of Hamilton, writes:
"But Burr was such a dissipated, libidinous character that Hamilton had a rich field to choose from in assailing his personal reputation. Aaron Burr had been openly accused of every conceivable sin: deflowering virgins, breaking up marriages through adultery, forcing women into prostitution, accepting bribes, fornicating with slaves, looting the estates of legal clients." [And they said even worse thing about him in the blogosphere.] The precise slur didn't matter, however: "Their affair of honor was less about slurs and personal insults than politics and party leadership."
So Burr called him out. They would settle the matter like gentleman, face to face, with pistols. Complicating matters was that Hamilton had declared an aversion to shedding blood in private combat and insisted that he would "waste" his shot, intentionally missing Burr. Was this suicidal? Henry Adams and various psychobiographers have argued just that: Hamilton was depressed and wanted to die. [New theory: Texas billionaire intentionally lunged into Cheney's line of fire.] Hamilton wouldn't practice with a pistol, while Burr practiced regularly. It was going to be a slaughter.
On a ledge above the river, the seconds of the duelists marked off ten paces. The two sides drew lots and Hamilton won. He chose the position that would require him to stare directly into the blinding morning sun.
The sequence of events remains controversial. Hamilton's second, a certain Pendleton, claimed that Burr fired first and Hamilton's shot was a reflexive spasm. But Burr and his second both claimed that Hamilton fired first. Indeed they claimed that several seconds elapsed before Burr returned fire. What's indisputable is that Hamilton missed far wide of his target -- severing a tree branch high above the ground -- while Burr hit Hamilton in the abdomen. Hamilton pitched to the ground and said, "I am a dead man," an accurate prognosis. Chernow believes that Hamilton intentionally fired first, wasting his shot in the most obvious manner, believing that Burr would have the chance, as Hamilton had written the night before, "to pause and to reflect." Wishful thinking. Burr was as sentimental as a copperhead.