And as for how they adapted the story to that:
Benoit didn't show up the show he was supposed to win the belt on, so they had Johnny Nitro/John Morrison/Johnny Mundo won it.
Batista kept the World Title he was supposed to drop until he got injured, & Kurt Angle won it instead.
Perro was not only the top heel in AAA, but he lead their top heel stable (Perros Del Mas), & was gonna have some huge feuds with the likes of Rey Mysterio Jr., but after his death, Pentagon Jr. (who was also in PDM), became the leader of the group, but AAA has kind fallen since Perro's death (though his death wasn't the only reason).
After Misawa's death & many other problems, NOAH has been on the brink of death. Although their last show of 2016 had some decent attendance.