I'm inclined to call BS on this one. Wouldn't the lack of a flash hole be appparent when the decapping pin hit and the case couldn't be sized? I seriously doubt they removed the decapping pin just because it was new brass.
Once fired from the same gun will yield better accuracy because the case will fit the chamber more tightly. But it will not be more forgiving of a dirty chamber or foreign object debris. I prefer 100% reliability over an extra degree of accuracy. I'm not saying that new brass is that much better, but it can't hurt. Also, I've never seen missing flash holes or other defects with Starline like I've seen with other brands (cough, cough...Winchester).
If your sizing new brass, why do you need to use the decapping pin anyway without a primer to punch out? I always back my pin out of the way when sizing brass without primers, less chance of messing it up. But, most importantly, I inspect all the pieces of brass before I load so I would notice a missing flash hole. I bought a bag of Lapua .308 brass and one had a flash hole drilled off to the side of the primer pocket. If I'd run the pin down on that round I would have broke it. So, your best bet is do what the books tell you to do... inspect the brass!