When I served in the military, it was common understanding that Hague convention required use of "ball ammunition" was desirable because you want to inflict casualties on your opposition, not necessarily to kill them.
From what I was told, a soldier wounded in service to a proper enemy army is useful to you because it takes a lot of people and effort to rescue, resuscitate and rehabilitate the wounded soldier than one you simply kill. Also having a screaming squad-mate does impact morale downwards too.
Of course, all that reasoning could break down when dealing with irregulars and guerrilla warfare, but possibly not.
In no way is it "Absolutely and totally false."