Judging by your photo, the primers were crimped in place by the manufacturer during the production process. I have never heard of that being done before on commercial brass made in the US. On military brass, yes, but never on commercial brass.
Several different manufacturers make a primer pocket swager that will clean the crimp out, but if I were you I would call Hornady and ask why the primers were crimped in on commercial brass. My guess is that they bought a load of primed brass or ammo from a non-US manufacturer, and it came crimped. Perhaps they'll offer to replace it free of charge. Worth a try.
If that doesn't work, you could look for a Dillon primer pocket swager to clean up the crimp, but that will be an expensive fix for a problem you will probably never run into again unless you reload once-fired military brass. A better option might be to find a nearby friend who can swage the pockets for you -- as I say, you will only have to do it once and will never do it again if you don't reload military brass. Or just replace the brass yourself and figure it's a "live and learn" situation.