This is an old phenomenon usually seen with long for caliber bullets, and I recall several old shooting magazine articles written on the subject. It was not uncommon for old 6.5 shooters to see this, and I have seen this with long 6mm's and the 69 to 80 gr .224 bullets.
The theory was the bullet did not truly stabilize, or "go to sleep", and eliminate or greatly reduce the yawing effects from being fired. Another theory was as the bullet slowed to a "sweet spot" for that bullet/load/caliber, it would shoot into smaller MOA groups at, say, 200 to 300 yards or whatever then the 100 yd MOA comparative would predict.
Once we learned we should all be using faster twists and bullets became better then we normally had in the "old days", much of this phenom dissipated. The occurrence of these interesting effects were difficult to always repeat, but they were seen enough to know they existed.
Some theories were based on drag effects and sonic shock waves at the bullet's nose, and there is some evidence to support areas of bullet flight that were more "stable" and less erratic then others. Bullet speeds in and close to the trans-sonic range may display this, and that is the theory behind the usage of "standard or subsonic" velocity 22 LR's at 100 yards vs bullets that start at supersonic and then transverse into sub.
All this is based on several groups and not a fluke 3-5 shot group that never repeated the phenom.
Another interesting idea around this phenom is chance bullet/load uniformity. Even today, a serious BR and LR shooter should weigh his/her bullets, check various dimensions for uniformity, load seating depth and runout, with uniform case length and neck tension, etc, etc. Sometimes, these factors come together for a few chance loads/shots and produce a surprisingly tight group that just happened to be shot at a distant target instead of the usual 100yd sighting. Often, this has led to the experiences we are discussing, and even today, I, and others, are often surprised to weigh a 100 ct box of "target" or "long range" bullets that have unacceptable weight and other variations. Example: a box of 200 grain modern bullets was weighed and the 100 ct was sorted into 6 different weight "groups". The extreme spread was over 3 grains!! and while the majority did fall within .5 grains of each other, any of the 2 to 3 grain variations would not be positive for even 100 yard best groups. Old hunting rifles would never show the difference, but higher end target type rifles and shooters would notice.
Try loading several random bullets/loads with less than perfect hunting bullets into a known sub 1/2 moa rifle and then shoot loads as near perfect as possible at twice the distance. YMMV, but you may discover how this phenom began.
Actually, this is why almost all us older BR shooters were also bullet swagers, for the factory match bullets of the day were not that great. Today is far better, but some brands and lots are better than others.
2 cents
