I've never had a 357 case separate on my, the only failure I've encountered was primarily cracks at the case mouth. I have had a few loose primer pockets over the eons too, but they seemed to be pretty rare in retrospect. If your cases are oversized in the web you can verify this by measuring the cases in that area and comparing the results to other cases from a different batch. I'd try measuring with a micrometer, rather than a caliper, but it all depends on what you have available.
If they're oversized, but otherwise in good condition you could try sizing them a little deeper by removing the innards from your sizing die, then screwing it in your single stage press upside down, then tapping a lubed case the die until it stops with a flat-faced soft hammer, or something like a nylon drift. Before you try this however, make certain you have a suitable rod handy to tap the cases back out of the die the other way. I've had to do this with old balloon head cases in my dark past. If you are doing this with a carbide sizing die, stop tapping the case in before it contacts the carbide sizing ring or you risk breaking the carbide ring.
The ring you speak of, is it just above the case rim, perhaps 3/16 inch or so? The brass could have been sized with a die that wasn't properly adjusted in the press. This can leave a bulge that sort of resembles a belt on one of the large old-fashioned rifle magnums. I primarily find these on 9mm cases that were sized in some of the more modern sizing dies that were redesigned when progressive reloading presses became so popular. These sizing dies have a much larger chamfer at the die mouth to help funnel the cases into the die. The downside is that they leave bulges near the base of the case which is what you might be seeing. I buy old (real old) Hornady Carbide Durachrome die sets, and equally elderly RCBS Carbides that have practically no chamfer at all at the die entry. Then I adjust these dies to cam over in my press to correct such issues.
Or, you could just toss the cases in the recycling bucket. Brass is still relatively cheap.