I've used the brass Winchester LRP's for Garand loads for the last dozen years with complete safety. Simply saying that a primer has been made more sensitive tells you nothing. Was it's sensitivity increased by 1%, 5%, or 10%? If you make sure you uniform the primer pockets of Garand brass and don't use Federal primers, you have a better chance of being struck by lightning than having a slamfire in a properly working M1 Garand.
When I bought my SuperMatch M1a’s, Springfield Armory provided a copy of Wayne Fattz’s article “The Mysterious Slamfire” which was printed in the American Rifleman in Oct 1983.
http://www.scribd.com/doc/2649554/The-Mysterious-Slamfire-
Mr. Faatz had an out of battery slamfire, from the clip, with Federal primers. He wrote an article trying to understand why it happened to him.
First on his list of slamfire causes is a sensitive primer.
1. Sensitive Primer (included under this category is a high primer)
2. Minimum headspace chamber and inadequate case sizing (leading to the firing pin hitting the primer with excessive force)
3. Hammer following the bolt
4. Fouled bolt face
All service rifles with free floating firing pins rely on primer insensitivity to prevent the primer from igniting when struck by a rebounding firing pin.
SKS’s slamfire so often there are lots of slamfire reports with SKS’s, Murray’s has a firing pin modification to reduce the chance of slamfires. Also, the SKS boards has this excellent “A primer on primers”
http://www.sksboards.com/smf/index.php?topic=56422.0
In the recent M1A manual: Springfield Armory M1A Manual, page 4
www.springfield-armory.com/download.php?asset=M1AManual.pdf
Ammunition
The M1A is designed and built to specifications to shoot standard factory military 7.62 NATO ammunition. The specifications for standard military ammunition include harder primers to withstand the slight indentation from the firing pin when the bolt chambers a cartridge. This slight indentation is normal. The use of civilian ammunition with more sensitive primers or hand loads with commercial primers and/or improperly seated primers increase the risk of primer detonation when the bolt slams forward. This unexpected "slam fire" can occur even if the trigger is not being pulled and if the safety is on. Use of military specification ammunition will help avoid this. Every shooter should use extreme caution when loading this or any other firearm. See page 17 for instructions on proper loading to help avoid a "slam fire". Also see enclosed article on “Slam Fire” written by Wayne Faatz
USATECOM Project No 8F-3002-04, Comparison Test of rifles, 7.62 MM, M14 Manufactured by Springfield Armory and Harrington and Richardson Arms Company. Author G. E. Hendricks, July 1963.
I have a paper copy of this report. The Army was testing production models of H&R’s and SA’s for dimensional part compliance, (part interchangeability), such things as the thickness of the chrome coatings were measures, rifles were reassembled after gaging and underwent endurance testing.
At round 5271 a Springfield Armory M14 went off out of battery. The report states:
“One rifle fired when the bolt was in the unlocked position causing breakage for the firing pin, extractor, bolt roller, ejector, and stock. The magazine split, causing the magazine floor-plate spring and 12 rounds of ammunition to be ejected against the bench rest from which the rifle was being fired. The case ruptured and several pieces of brass were found in the area. A broken part of piece of brass perforated a cardboard box with was position between the gunner and the proof director. The cardboard box was used as a brass catcher. Not all the broken pieces were found. Although no one was physically injured this is a seriously unsafe condition.”
This is the only data I have found on slamfires and mil spec primers. Out of 35,000 rounds fired, one rifle slamfired out of battery with a mil spec primer. Therefore I estimate the odds of having an out of battery slamfire to be 1:35,000 each shot. Using more sensitive commercial primers only increases the slamfire probability, by how much, I don’t know.