It's a little hard to grok the details, but it sounds like it's a collection of "dead drops". Like, if done in a physical way, imagine locations around a city where you can drop off scraps of paper with cipher encoded message on them. Encoded not just with sender/recipient keys, but a dead drop location specific key too. And an agreement that replies to a received message get dropped off at a different, randomly selected one.

Everyone can see and read the cipher text on all the papers, but each of the 4 people can only decode the things meant for them.

So, if that's how it works, you could certainly learn who was talking to who if you had access to all the devices. But access to one device only shows you what came and went to the device, but no data about which of the other three users were involved in those reads/writes. You would have to gain access to each device, in turn, to prove whether it was in contact with the first device.