Laurie and Jon's relationship is public, with no privacy, physical intimacy or affection, while HJ and Nelly's was secret and private, and the two men are obviously very intimate with each other.
It also gives Alan Spousal Privilege, meaning that anything Denny tells Alan can remain secret/private as Alan cannot then be forced to reveal it in court.
While the two major players of the game, SEELE and Gendo had private, secret agendas which ultimately failed, everything occurred just as planned by a very hidden player, Yui Ikari.