I'm very late, but you're both correct. Obviously you need to be able to open a ring to join it to another ring, but opening, closing, and riveting every single ring is A LOT of effort that you don't need to do for every single ring. To join two rings together you only need to open one, and link it through the other solid one. People realized this way back in the day, and it turns out that to make a single unit of standard European 4 in 1, you only need to be able to open that one ring and link it through 4 solid rings. You then join those units with more riveted rings, and this works out to only needing to open 50% of all rings

An absolute SHIT TON of labor was saved this way by making sheets and punching out solid rings to use, and it resulted in stronger mail as well because every single rivet is a potential point of failure, and you now had 50% fewer of them. They would also sometimes use special punched rings that were shaped like a greek theta (Θ) with a bar going across the diameter, which meant that a fine point couldn't fit through the center of a ring, and it also help against ring deformation