Ahhhh... Maybe that's it.  The debate on thicker cups arose from discussions about slam fire in Garand Rifles due in part to the floating firing pin slamming against an overly sensitive primer with a thinner cup... as I recall - the discussion was that the Federal primers were the most susceptible to this, and the CCI primers were the safest.  I might have mistaken or miss-quoted this... but that's how I recall it anyway.  Either way, I'll be using the 34s in my Garand loads from here on out.