In a recent video on former CSK star Badrinath’s YouTube channel "Cric It with Badri",
he shared his experience of who actually makes the decisions.
Link: https://www.youtube.com/watch?v=MDksa3LXelE&t=563s
Translation:
Back when I was on the team, Fleming wouldn't even be the one to tell me when it was my turn to go out and bat; Dhoni was the one who handled that. Once the time came—say, after a certain number of overs—Fleming would go up to Dhoni and ask, "Are you going in, or should we send Badri?" Dhoni would then make the decision: "Okay, let's send Badri now—is this the right situation for him? Or no, I'll go in myself; tell Badri to hold on." Fleming would simply relay the message to me: "Dhoni is going in, Badri; you'll have to wait a little while." So, it was always MS Dhoni; he was the one who made those calls. That is why I feel his absence is a huge loss...
Bonus point that I found interesting:
Another point—is Fleming actually interacting much with the Indian players? Is he engaging frequently with the youngsters? Is there a genuine dialogue or line of communication? For instance, regarding Urvil Patel today: was there any communication telling him, "You need to bat in this specific manner," or "Rabada is bowling in this specific way—you can play this shot, but you shouldn't attempt that one"? I find myself doubting whether such communication actually exists.