Without knowing anything about that exact chain, I think you analysis is probably right on. Mushrooming the rivet heads would make for a chain that is less likely to come apart, but it would also take more force to press a rivet out. I bet you can break it with a normal chain tool, but I wouldn't try to reassemble it using the pin you pressed out since the flange is almost certainly shot. This sounds like a perfect time to use a master link.

Given how much of a pain that sounds like, why not just scare up some kind of normal chain that can be cut and reassambled without worrying about mushroomed heads and stuff?