He didn't throw it away intentionally. Biographies and other research I read 15 years ago proved that Hamilton had the hair trigger set on the gun to get his shot off first. The result was that the gun went off early. There is still some question as to whether or not this was considered "cheating" at the time.
Found it. The article that got me interested in this was "Pistols shed light on famed duel" from the November, 1976 Smithsonian magazine.
I believe you are correct. As the story goes, way back in 1976, as the country was celebrating its bicentennial, the two pistols were being examined before being placed in the Smithsonian. Upon close inspection, Hamilton's pistol was rigged with a hair trigger, requiring only 1 to 1.5 pounds of pressure to pull, unlike the 10 to 15 pounds of pull required to fire a normal (unaltered) pistol. As a result, a duelist would have an incredible advantage over his opponent. In this case, it seems, Mr. Hamilton held the gun a bit too tight and triggered it before he had aimed, hitting the leaves above Burr's head. So, it would seem that although the fix was in, Mr. Burr's luck overcame it. Hamilton's nobility is, in my mind at least, somewhat suspect.