Yeah, it's a concern!! Here's two failed 9.3x62 cases I had from one magazine-full while practicing rapid fire one day with my Model 70 Classic Stainless. I didn't notice the first failure. The second, more extreme one blew junk back into my face and popped the floorplate open. I sent Hornady pics and they tested samples from the same lot as my brass and concluded there was nothing wrong with the production run. Both cases were on their third firing when this happened. The bullet was a 286gr Partition loaded to modern pressures with 64gr of Big Game. Rob at Western Powders told me that not only were my loads safe, but that he'd never seen a case fail through the head the way these two did. I checked the chamber with my bore scope, thankfully no damage, and the bolt face was fine as well.
After a bunch of phone calls and research I discovered there were two problems. First of all, Hornady saves a buck by making 9.3x62 brass from '06 blanks. As kk alaska points out, '06 brass is undersized at the base compared to the 9.3, by how much I can't remember as my notes aren't handy at the moment. Secondly, the RCBS dies I was using at the time size 9.3 brass down to the dimensions of the '06 case. Come to find out this is because RCBS used to make forming dies to create 9.3x62 brass from .30-06 cases. Fifty or sixty years ago this worked great because it allowed a guy to make cases for the old Mauser Uncle Bill brought home from the war. Today however, it's a liability because the growing popularity of the old 9.3 (as discovered by that wonderful Barsness fellow) is predicated on loading the round up to modern pressures.
So I've concluded that if you're content with using the 9.3x62 at its old school pressures, Hornady brass or RCBS dies are probably okay. However, if you are looking for the performance we've all come to expect avoid Hornady brass and RCBS sizing dies. The Hornady brass is no good from the outset, and the RCBS dies will ruin brass is that is properly spec'd to begin with. You need to use dies which are sized to the CIP spec. I know that Lee and Redding dies are. Supposedly the Lymans are as well, but I don't know for sure. Proper brass is anything but Hornady.