Whenever I read a question like this, my answer is ALWAYS the same!
Watch slow motion video of the elite pitchers and decide for yourself.
Slo-mo video is your truth detector! Compare what people tell you to elite athletes and see if it's true or not.
Personally, I have studied 100's of pitching clips and EVERY elite pitcher uses their back hip to "close the door" as you mentioned. In some pitchers, that closing action is easily seen in live action, in others, the hip snap is so quick that you can only see it when you slow the video down.
Don't take my word for it...see for yourself.