Its a non-issue. The pierced primers are a sign of pressure in the other direction from the backed-out primers. I have seen asymmetrical in many of my rifles. I just full-length size and reload-on. Granted, case life for me (generally) is around 3-5 loads with Remington and Winchester brass. With HXP and PPU, I have some cases going on 7 loadings. HXP and PPU is much better brass than the current US commercial stuff. I have a couple of hundred loads consisting of Hornady brass, and am now up to 6 re-loadings with those. Pricey, but good stuff too.
As always, use the most current load data, and never exceed the maximums listed in the manuals. Almost all of my loads are in the 80-85% of maximum. I keep the velocities to around 2200 to 2300 FPS. Remember, these are old rifles, and there is no need to max the loads.
Heck, I have a 220 Swift that bulges cases in an asymmetric way, and that thing still shoots 1/2 inch groups all day long. Cases life is short for that one, as I max all of those loads for varmint hunting.