I think this is true. I also think there would naturally be some stubbornness or "well, I'm the coach, I decide who's on the field".
Who knows, though. Saying for sure one way it another would be pure speculation on our part.
Given that Rivera was on the way out in week 4 I doubt he feels like he can tell his boss to back off since he is the coach. From his previous discussions about asking for help from Madden and others during the off-season I really doubt he wouldn't listen to Gettleman and take his advice.