Sorta - we do
http://www.thegunzone.com/hague.html
While we do not use bullets manufactured at the DumDum arsenal, India - we DO (legally) use "open tipped" sniper rounds.
From the JAG opinion
"The purpose of the 7.62mm "open-tip" MatchKing bullet is to provide maximum accuracy at very long range. ... Bullet fragmentation is not a design characteristic, however, nor a purpose for use of the MatchKing by United States Army snipers. Wounds caused by MatchKing ammunition are similar to those caused by a fully jacketed military ball bullet, which is legal under the law of war, when compared at the same ranges and under the same conditions. (The Sierra #2200 BTHP) not only meets, but exceeds, the law of war obligations of the United States for use in combat."
This use is legal, in part, because we are fighting non-uniformed combatants....Link is for more information.
The squad-level grunt does not have access to this ammo, it is also the wrong caliber for the M4/M16 and I doubt that the 240G drivers are given match grade ammo to burn thru their weapons.
So, yeah, the story is BS as printed.