Yes indeed, Winchester's production machinery was inspected by Berettas engineers and scrapped. The gauges, fixtures, and production flowcharts were the "gems". Beretta designed and built the production machinery they used for M1 production in house, and had never done so beforehand. They started production using statistical process control, which I believe Springfield Armory hadn't incorporated yet.
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By the 1950's Springfield Armory was a completely inept organization; hopelessly stuck in their old ways and completely unwilling to change for anyone. They fought the DOD for a long time and rather than getting things their way, they were shut down in 1968. It's really sad that we allowed that to happen, but it is what it is.
I have fired a few Beretta Garands and have found them easily the equal of any other service grade Garands I have ever shot. I have read from others that the Beretta Garands were superior in overall quality to US wartime Garands. There could be some truth to that, but I doubt the difference was really significant.
There are lots of tales of Beretta's being more accurate than US Garands. With good quality ammunition, I never found this to be true. Now if using USGI ammunition made before around 1970, then yeah, chances are most others were more accurate. The issue with the Garand's accuracy was never the rifle. But USGI ammunition in WWII was (in some ways) rather low quality. The overall cartridge was just fine, completely reliable. The issue were the bullets. I have pulled bullets from .30M2 rounds from 1940 all the way to the mid '60's and I have found as much as a .003 difference in bullet diameter! Not even Russian ammunition had bullets that bad. (in all seriousness, Russian 7.62x54 was very high quality ammunition, making Mosin Nagant's a bit legendary for accuracy).
Because of this, the acceptance standards for the Garand during WWII was 6 MOA (IIRC), which is a good deal less accurate than an AK. However, with good ammo, most would shoot about 2.5 MOA with no trouble.
The Beretta's I shot were every bit as accurate as any GI Garand I ever shot.