finally remembered to get out the caliper and do some measuring. The diameter of the rim was the same on the caps and on some randomly-selected .380 cases, .370 to .373". For thickness I set the caliper along the taper of the case to the extractor groove, and got a difference. The snap caps measure right at .034, the cases fell right around .042".
So I'm guessing the thinner rim let the extractor of this pistol slip over instead of grabbing.