NFL teams all have coordinators but some coaches prefer to take play-calling duties under their own jurisdiction. 

Especially coaches who specialize in one side of the ball. For example the Packers HC Mike McCarthy and the Saints HC Sean Payton (currently suspended) both call the offensive plays for their respective teams because they were both hired for their new age offensive ideas. Whereas the NY Jets HC Rex Ryan was hired for his defensive knowledge and he calls all of the defensive plays. 

In all 3 of those examples the other side's play calling duties (defensive for McCarthy/Payton, offensive for Ryan) are run by the coordinators.

And on a tanget, a lot of the details in the series are kind of suspect from a football strategist/analyst/nerd point of view. At one point, Halawa has game stats of 8 catches for 108 yards and 2 TDs. Meanwhile the 2 TDs of Halawa are mentioned to be for X and Y yards. (I dont remember the exact details, also it might have been Hawick) And X and Y added up to 106 yards. After reading this I seriously sat for almost 5 minutes trying to figure what kind of situation would have a receiver catch 6 balls for only 2 yards. 

(If youre not a football fan, any time the ball is thrown backwards or sideways its considered a handoff not a pass and so for Halawa, or Hawick, to have the other 6 catches go for only 2 yards there would need to be some kind of situation in which she either ran backwards multiple times or caught the ball for such a short distance that it was called no gain multiple times)