That bit about "eccentric" chambers is more than a bit off.
I suspect that this condition was assumed after examining fired cases with odd bulges near the head.
I have several drawings of "official" .303 chambers. I loaded the data into AutoCad on individual layers and then added the SAAMI data. No huge differences, just a few minor differences at the shoulder/ neck / throat area. (BTW, if anyone has chamber / barrel drawings for Bren, Lewis and Vickers barrels, I would like to expand the exercise. In my experience, machine gun barrel chambers are generally different from rifle chambers for the same cartridge.
What I suspect is that there were tooling variations, especially during wartime. Given the cost in time and labour to produce reamers, especially Pre-CNC, it would not be unreasonable for new reamers to be made a bit oversized.
This would allow the reamer to be resharpened a few more times before being scrapped as unusable.
Couple that with the common occurrence of "undersized" brass and some fired casings look seriously ugly.
Given also that military users are not known for reloading brass scavenged from the two-way rifle range. nobody really got too bent out of shape over the issue. Added extra reason for letting brass lie, would be the corruption of most (Commonwealth) .303 brass by mercury in the primer.
What still intrigues me is the horrendous tolerance on the groove diameter in .303 barrels. I think it is a hangover from the days of the Minie ball and P-53 Enfields. Yes, bullets (open based military ones, anyway) DO expand when booted up the backside by 45,000PSI or so. However, one cannot guarantee that said expansion will be absolutely concentric. Maybe the idea was that as the lands impressed into the bullet jacket, the displaced metal would flow outwards to fill the barrel grooves. That is vaguely possible, but see concentricity caveat above.
However, in the bad old days of cupro-nickel jackets, black powder and Metford rifling, complete bore obturation was very unlikely. Adding Cordite, which burns at a very high temperature, to the situation only made things worse by cheerfully eroding out the throat as the gases ate their way around the base of the bullet.
So, They changed from a perfectly functional form of rifling to a cruder system that worked with the ammo that was available. (Bullets are cheaper than barrels!) Note that the Type 38 Arisaka 6.5mm used Metford style rifling, (Your Arisaka barrel may not be "shot out";l it just looks that way)