Actually it isn't that the receiver on the Enfield which "flexes" very much but rather it is the BOLT which compresses somewhat. Receivers on Mauser type Rifles with Front locking lugs (especially those with an internal magazine) flex quite a bit.
Here is the following from another forum from an High Power Rifle competitor from Bisley:
#4 Accuracy
Accuracy keeps cropping up on this forum. I own a number of military and sporterised #4's (and a half dozen or so SMLE's) Other than the mint Irish #4 Mk2 shooting Sierra 174 match bullets, the accuracy of these rifles is fair (3" to 4" at 100 yards).
However, the #4 has been used as a target rifle. When tuned up by a master armourer who knows his trade, these rifles can be made quite accurate (under 2").
At long range the #4 rifle comes into its own. Until recently (1990) the #4 was the only rifle to use at long range, because it would "compensate". (I should point out that these rifles have all been equipped with heavy barrels in 308, but until about 1958 we shot similar rifles in 303.)
A well tuned #4 rifle would should a vertical egg-shaped group at close range, so we would use a front-locking target rifle at close range (300 to 800 yards). At long range we would change over to our long-range rifle - a #4.
Now, you might wonder how a big group (say three minutes) at 100 yards can become a one minute group at 900 yards. On the face of it, it defies logic. The key to the puzzle is barrel compensation. Suppose you are testing ammo at 100 yards, and you shoot loads with 34, 35 and 36 grains of powder. In most rifles each hotter load will print a bit higher on the target. Not so a Lee Enfield. The rear locking lug leads to a "springy" action. The muzzle of any rifle is vibrating and moving in the vertical plane when fired. In a #4 the muzzle is moving "up" as the bullet exists the muzzle. Assume ammo with some variation in velocity. A slow bullet leaves the muzzle later and the barrel has moved up more. The slow round is aimed higher. At short range it prints higher on the target than a fast bullet which exists before the muzzle has moved up as much. At long range the effect of velocity variation causes a vertical group. However, with a #4 the slow rounds were aimed higher, automatically, so they arrive on target. The faster bullets would normally printer higher, but in a #4 they were aimed lower, so they too would arrive on target.
If this strikes you as myth, wishful thinking or hokum - welcome to the club. I grew up listening to stories of "compensation' at long range and was skeptical. I served a hitch working in a ballistics lab and learned that many a theory was just an over-reaction to an anecdotal event. Only a controlled experiment can determine if an observation is statistically valid.