That is so crazy about the affair spouse getting so worked up that the betrayed spouse snoooped into the affair. I would say that the affair is a much worse betrayal than snooping. I guess from their perspective, they are in fantasy land and dont want you bringing reality into it by snooping and discovering it. You intruded into their own personal fantasy life.
If you are going to rebuild following an affair, I believe that the betrayed spouse needs open snoop access to many things so as to help rebuilt trust. The affair spouse needs to open up their life to the betrayed spouse during this time.
As far as the snooping from the betrayed perspective, it probably is ok in some situations to bring the A out into the open so it may have a quicker chance to fade, however, continually snooping is only going to cause hurt to the betrayed spouse as the A continues.