The Rhinos lost 66-10 at Castleford last week prompting Hetherington to say he was "not stubborn enough to believe no change is always the best option".
"Something needed to be said after such an ugly day. Gary cleared it with me," McDermott told BBC Radio Leeds.
"I've got no drama with anything he said in it."
He added: "There are some lines where you might think 'what does that mean?' I think what Gary is saying and what we are saying is that we are not going to just change after one bad day at the office.
"For me the biggest thing about the Castleford game was they were white hot. We shouldn't be conceding 66 points but don't get away from the fact that they were brilliant on the day."
McDermott led Leeds to the treble in 2015 but they struggled last season, failing to finish in the top eight in Super League.
Hetherington said in the letter that he would be in a "better position to make an accurate judgement on the performance of all our players, coaching staff and senior management including myself" after their next four games.
The Rhinos, who host Catalans on Friday, have lost two and won two of their opening four Super League fixtures.
Leeds Rhinos coach Brian McDermott says he is "cool" with the open letter chief executive Gary Hetherington released to fans earlier this week.