As with so many things Army, it was probably a garbling of a command found in a manual-which nobody has read for 40 years or so-that was then handed down and passed from mouth to mouth until it became Gospel Truth. I ran plenty of ranges and I never had any formal instruction, it was always "watch the experienced guys." or remember what you saw in BCT.
When I went through BCT at Fort Dix in the Summer of 1967, if you fired a tight shot group-all 3 rounds touching with the M-14 on the 1000 inch range you had fired a "Ballantine group"-named after a then popular brand of beer whose logo was 3 rings touching. However, it was available only in the Northeast NJ-NYC area, when I mention to veterans who went through BCT at other posts, they give me a blank stare.
2 phrases from the black powder era are still with us-"Lock, Stock and Barrel" and "going off half cocked".