That said, an M1 Carbine is neither of the above, and even though the stock GI irons are graduated out to 300, I would wager that the vast majority of people who've ever tried one at that distance would be impressed with the results of the video in question...which actually kind of reinforces your point about irons being adequate when somebody knows what they're doing, and in this case, he certainly does. Your analogy to an AK is not a bad one considering the inherent accuracy of the two designs (I might even give the M1 an edge), but it's also probably worth considering that with a 100 yard zero, at 300 yards, the drop of a .30 Carbine round (~48") is almost exactly double that of a 7.62x39 (~24").
That modernized AK with an aluminum C-More is my favorite rifle. Originally I just got it to learn the platform while shooting 3-gun matches.
(1) You'll note that the rear sight, as seen by pausing the video, is the well-made original sight, not the cheap bent-metal version issued later on. Maybe the later ones were also rougher than this Inland one?
(2) Taking particular note, you will see that the rear site had to be drifted way to the left to make up for either a bent barrel, or a receiver not accurately threaded to line up the axis of the bore with the axis of the bolt. With the rear sight centered, it would sight in way to the right. My carbine was like that, too.
(3) With the sight path set in the midst of a heavy woods, there probably would be much less cross-breeze. IMHO, from old times the carbine was not as accurate in gusting winds as the M1 Rifle. (Later on, as a rifleman I qualified Expert with it also. It shot better in the open range than the carbine.) Perhaps this factor was helpful in getting a good pattern?
(4) The carbine was a much better and cheaper weapon than the .45 pistol for truck drivers, officers, cooks, rear echelon clerks, etc. with not enough time to train recruits in the niceties of pistol shooting. Yet even mortar and MG gunners still needed both hands to carry and set up crew-served weapons, so they were armed with the 1911A1 and protected by riflemen. Training for marksmanship with the carbine was pretty much the same as for the rifle or BAR, so one could be sent to the line with enough skill for a real weapon.