Only real source I can find for this mentions it as a single incident:
"By 12 March, when the 204th Airborne Brigade began to cross into German territory, it came under intense small-arms fire, punctuated by artillery. The German actions inflicted heavier and heavier casualties as the missions continued over the next few nights. The Germans also noted the flight of Soviet transport aircraft into areas behind their own lines, evidently dropping supplies to the advancing airborne groups. Some troops without parachutes were also dropped during the course of the operations. Slow-flying U-2 biplanes would skim close to the ground, and the paratroopers would leap off into deep snowdrifts. The first major attack occurred on 15 March when the garrison at Maloye Opuevo was overrun by about twelve hundred paratroopers from the 1st and 204th Airborne Brigades."
Wasn't it in the history of the Russian sniper from that time?
It is from the movie Enemy At the Gates, which is at best, not very historically accurate.
It long predates that... It was reported during WWII.
Not saying the reports are more accurate, I really don't know.
I suspect it was a bit of propaganda that meshed with Russia having massive logistics issues at the start of the war.
You are correct on both counts, that the myth far predates the movie and that it does have a basis in the actual reality of logistics and production quality problems for other Soviet equipment.
I was going to expand on this more but got caught up sperging out about Star Wars canon in another thread lol.
I think it is fair to say that, at this current point in time, Enemy At the Gates is probably the most widely known, most popular piece of media responsible for the 'Russians only had 1 rifle per 2 or 3 soldiers' meme.