I think, in the specific example of a Case soddie, it's called a 'compression rivet' (two pieces, a 'male' and 'female' side, press-fitted together). Some other makes use a 'bird's eye' fitting, which I think is a threaded nut-and-bolt type of fitting, screwed together and then the exposed ends are cut/ground off. Both are fairly large in diameter.
I'd bet the large diameter of the pivot rivets on any of them is a necessity because it's the only hardware providing any strength in the pivot, due to the absence of bolsters. In other knives with metal bolsters, the bolster itself adds a lot of lateral strength as an anchor for the pivot pin, so the pivot pins themselves don't necessarily need to be as huge. If the soddies used the same size pins as on other bolstered knives, the pivot would easily pull apart with sideways pressure. The delrin or wood handles on a soddie aren't anywhere near strong enough to anchor/support a smaller pin.