But they didn't move everything, they just invaded Steelport. Although if you go with the uh... killbane ending I could see your point, but the fact that Boss is now president means that, that ending is most likely forgotten.
You are aware that Saints Row IV is simply Saints Row the Third: Enter the dominatrix rebranded and extended on?
http://saintsrow.wikia.com/wiki/Enter_The_Dominatrix
Basically the plotiline was meant to me non-cannon.
Meaning the game's storyline is going to be completely irrelevant.
Just Saying