A head coach will inherently interfere with a coordinator if the coordinator needs a serious, dedicated approach from his players to run his unit, and the head coach, who has more organizational power than a coordinator, establishes a lax, silly team culture in which the players in general aren't sufficiently serious and dedicated and accountable.
None of this prevents Fangio from holding his defensive players accountable to his (Fangio's) own standard.
Fangio had the power to run his defense as he saw fit, including the "culture" for the players on the defensive side of the ball. If he chose not to exercise that power - possibly because he was checked out and never wanted to be in Miami in the first place - he is responsible for that failure.
When you are in charge of the defense, you do not get to blame "culture issues" on someone else.
It was Fangio's job to establish a culture of accountability for the defense, and (according to you) he utterly failed to do so.