I looked at the photos of these defevtive snap caps in your link, and they are clearly marked "Cal. 20 Made In Italy" just as you said.
So we are down to needing the measurements that Daryl asked for in order to determine just what is going on to permit these snap caps to fall well into the chambers of three different 20 gauge guns. I'd be most interested in the largest diameter of these snap caps, and the diameter of them at the end.
My first thought was the possibility that this was a gun you had never fired, and that it might actually be a 16 gauge. Being a J.P. Sauer made that possibility even more likely because of the popularity of the 16 gauge in Germany. And I have bought several guns that turned out to be a different gauge than advertised. When I bought my very first Syracuse Lefever, I got it from a guy who inherited it and knew nothing about it except that he didn't want it in his house where his grandkids might find it. It was so light and trim that I was sure it was a 16 gauge. When I got it home, I dropped a pair of plastic 16 ga. snap caps into it to drop the hammers, and they fell into the chambers. I had gotten very lucky on my first Lefever purchase by getting a very scarce small frame 12 gauge gun.
The fact that you tried these snap caps in two other 20 gauge guns kinda blows that theory out of the water. But the different depths that your caps went into these different chambers just goes to show the variability of chamber and bore dimensions that we deal with. Another possibility is that there was a manufacturing screw up, and some 28 gauge snap caps somehow got misprinted with the "Cal. 20 Made In Italy" marking. I've personally seen a number of such screw-ups made by human error during the changeover process in manufacturing. Again, I would beg, borrow, or buy a micrometer or digital caliper to get those measurements.